School in Germany starts when kids are six years old. Germany has compulsory education - thus there's no chance for homeschooling. Theoretically, the police may even force kids to go to school. (It actually has happened, albeit in few cases, with kids of members of radical sects who objected to sexual education in schools.)
There are no school uniforms, although some people are toying with the thought since in recent years, more kids have been bullied because they can't afford the latest brand fashion. However, others are a little iffy about putting children into uniforms 
One important thing: Unlike most countries in the world, school in Germany only happens on half of the day, pre-noon - at least until the students reach the 7th grade; from then on, school usually finishes around four in the afternoon. In order to cram all the necessary lessons into these few hours, school also starts earlier (around 8 o'clock, mostly, though students in higher classes may also start school at 7 a.m. on some days). Ganztagsschulen (all-day schools) are demanded by some people, but are still a minority. Thus, school lunch / dinner is a thing mostly unknown in Germany and German students generally don't have the same level of attachment to their school that Japanese students (for example) have.
Another important thing: The schools are run by The Sixteen Lands of Deutschland. Which means: School works a little differently in each German state. This of course leads to problems if a kid moves from a state with a less demanding school curriculum to a more demanding one.
Ve inwented zis: Kindergarten
Precursors to the kindergarten have been around since the late 18th century, but it became a pressing issue during industrialization, when many mothers had a) to work all day and b) no other relatives who could care for the kids. The word kindergarten (a garden for kids) was coined in 1840 by a Friedrich Fröbel, who also founded the first kindergarten. In 1851, the Prussian government banned it, fearing atheistic tendencies. The ban didn't stay for long though, and from then on, the number of kindergartens started to grow continually - under all governments, whether monarchist, democrat (left or right), national socialist or communist.
Other countries (in fact, most developed countries) copied the concept, with some variations (most importantly, the age of the kids: In Germany, kids usually start going to the kindergarten at the age of three).
The basic: Grundschule
At the beginning, things are relatively easy: All six year-old kids (well, almost all) start at the Grundschule (lit. "basic school"; primary / elementary school), which is four years long (except in some states, where it's six years - thanks to the German federalism). Towards the end of it, kids are tested for which type of secondary school they're fit. (This is a very controversial topic.) Because yes, there isn't just one type of secondary school in Germany. That'd be too simple.
Note that recently primary schools have started teaching English to eight year-olds.
The main school (well, once, not anymore): Hauptschule
Developed from the old Volksschule (people's school), which used to be eight years long, including the four years of Grundschule. Now the time spent at the Hauptschule is five or six years long. The type of education you get there is more practical, intended as a preparation for a life in the work force. Once, the majority of people went to this type of school; today, only a minority does, and in some cases (esp. in big cities) the Hauptschulen have become "problem schools". Not as bad as American ghetto schools, but if you listen to some people, almost as bad. It's considered the lowest level of school education and to graduate from it is regarded by many people as not much better than not having graduated at all. In recent years there have been developments to scrap this type of school completely in many states, a suggestion which is being opposed by traditionalists.
The diploma is called "Hauptschulabschluss" ("Abschluss" meaning Graduation) and achieved after passing the 9th grade.
Nowadays many schools offer a special class which can be attended after passing the 9th grade and which makes is possible to achieve the next better diploma. (see below)
Let's get real: Realschule
For a long time, the only schools existing were Volksschule and Gymnasium, but nothing in between. Some people criticized this and demanded a new type of school for kids who were supposed to become neither menial workers nor intellectuals. Since said new school taught the "Realien" (old term for physics, geography and history), it was called Realschule. The idea came up during the time of enlightenment, and the first one was founded in 1747. In some places, it was also called "Mittelschule" (middle school).
For some time, the Oberrealschule (upper / higher Realschule), essentially a Gymnasium without Latin, also existed. In 1964/65, they were turned into Gymnasien too (which rather meant that since then, a Gymnasium doesn't necessarily have to teach Latin anymore, not that the Oberrealschulen all introduced this old language to their curriculum.)
Note that in recent years, most eastern and some western states have lumped together Hauptschule and Realschule into one kind of school, which tends to have a different name in each country.
The diploma has different names, varying from state to state ("Realschulabschluss" and "Mittlere Reife" being the most common) and is achieved after passing the final exam after the 10th grade. With this diploma you can attend a Gymnasium (not all Gymnasiums offer this), Berufs(ober)schule or Fachoberschule (the latter is for people who want to study at a Fachhochschule, a school of applied sciences but considered a watered down university, with a focus on practical experience, even though studying certain subjects at a normal university after graduating is possible). Depending on the state a certain grade point average is required for each/some of the mentioned schools. Yes, that's German federalism.
However, some students choose to start working after graduating without further education.
Education Mamas want this: Gymnasium
The Gymnasium (another old term is Lyzeum) is, so to speak, the highest of the high schools in Germany. It developed from the old Latin schools which were mostly run by the church. The Gymnasium was supposed to prepare students for their later studies at a university (or for a clerical job). The British equivalent would be a grammar school. Subjects like German, modern languages and sciences were only added to the curriculum later on. Latin (and ancient!Greek) were still considered important. Later, variations like the Realgymnasium were introduced, which had less emphasis on the classical stuff. Even nowadays there are humanist Gymnasiums (which still teach Latin and Greek) as opposed to Gymnasiums which prefer modern languages and/or sciences. There are also Gymnasiums specialized in areas like music or sports, though they're pretty rare.
Completing your education at a Gymnasium usually takes nine years. Together with the four years of Grundschule this adds up to thirteen years of education - in most countries of the world, it's just twelve, as was the case in East Germany. After the German unification, some eastern lands like Saxony and Thuringia kept the old twelve years, which meant an eight-year Gymnasium (short: G 8). Then some western lands started copying this system, and later, the rest followed. As of 2010 this process is concluded in half of the lands and on its way in the rest. (Which means that some eastern lands had to change their school system twice in less than twenty years.) Critics state that the shortened Gymnasium leads to even more stress for students, in some cases going as far as burn-out. Since the transformation was often rushed and not well planned, it usually means learning the same stuff scheduled for three years in just two.
Originally, only a small minority of children went to the Gymnasium. Nowadays, it's often about half of the young population, depending on the region. Still, the Gymnasium has retained some prestige. After all there is no higher school around, at least none that is state-run.
During the last two grades of Gymnasium the old classes are dissolved and students will take courses instead: Leistungskurse (achievement courses, mostly two, in some states three), which take five or six hours per week, and Grundkurse (basic courses), two to four hours per week. The Leistungskurse make up about half of your Abitur grade.
Originally students had a lot of freedom choosing courses and discarding subjects they disliked, but by now the reform of 1972 has been reformed itself several times, to avoid students discarding core subjects. Nowadays German, maths, English, one science, and another science or another foreign language along with one social science are all obligatory, as is physical education.
The diploma you get after passing the final exams is called Abitur (short: Abi), derived from Latin abire (=leaving (the school)). Which is celebrated big time, of course. Often, the students will do an Abistreich (prank), making fun of their teachers, which is tolerated as long as things don't go too far.
A compromise: Gesamtschule
Not everyone liked the three-parted school system. Critics stated that this system was too classist and may encourage elitism. So, starting in The Sixties (but it only really took off in The Seventies), politicians of the Social Democrats and Liberals created a new school, the Gesamtschule (roughly: comprehensive school) - one school after Grundschule, for all kids, from all classes and backgrounds. Other than in Britain however, the new school didn't replace all other school types, but instead co-exists with them. Thus, parents who didn't like this new-fangled concept, still sent their kids to the schools they knew. And inside the new schools, kids were divided into courses or classes which would teach at the level of Hauptschule, Realschule or Gymnasium respectively - the old divisions lived on. And of course, different Länder (with governments from different parties) implemented the new schools differently - leftist Berlin has many Gesamtschulen, conservative Bavaria almost none. Critics pointed out that the students from new schools would score lower in tests.
Nowadays, the Gesamtschule is still around and a controversial topic. Prepare that even Godwin's Law may be involved in discussions.
For special people with special needs: Sonderschule
Sometimes also called Förderschule (assistance school), these are schools for kids with mental or learning disabilities. About 5% of kids attend this kind of school. Hospital schools, which take care of children's education while they're recovering from illnesses, also fall under the "Sonderschule" category, as do teachers who teach single students (for example those whose health is so delicate that they can't go to school, or students who are unable to go to normal schools due to behavioral or psychological reasons).
For the job: Berufsschule
The Berufsschule is part of another education system called "Ausbildung" (apprenticeship). See below.
Keep this in private: Privatschulen
For Brits: What you'd call a "public school". Private schools are somewhat uncommon in Germany - in 2006, only 6% of all students went there. The state supports them financially; still, parents will have to pay money to send their kids to such a school. Some of them are specialized schools, centered on music or sports; some of them supposedly have the purpose of helping spoiled brats from the upper class finishing school when the state schools (just them?) failed.
Even though there're so few private schools around, in fiction they're over-represented. There are some series of kids' books set in boarding schools, like Burg Schreckenstein (set on a castle - now that's a pretty cool school...), TKKG, and the classic book Das fliegende Klassenzimmer (The Flying Classroom) by Erich Kästner. Serious literature also has some examples, like Young Törless or the recent One-Hit Wonder Crazy.
In recent years, more private schools were founded, and more and more parents are sending their kids there.
Try it again: The "Ehrenrunde"
This seems to be a German phenomenon (and is a reason why Germans spend more time with education): Students who didn't do so well (read: abysmally) in one year may be forced to repeat a class. Typically, this happens if they get one 6 or two 5's (grades are on a scale from 1 to 6) on their report card. If people fail a year more than twice, or a third time, they will (typically) have to leave school altogether, without any degree. Consequences: You'll be in a different class than your friends now.
Oh, BTW: "Ehrenrunde" means "lap of honour". Yes, it's ironic. The regular term is "Sitzenbleiben" (='remain sitting').
And another thing: Der Spickzettel
German youths occasionally find tests too hard, too. One possible solution: Prepare a piece of paper, the Spickzettel in German, write the important stuff in very small letters on it, and use it during the test without being caught by the teacher. The attitude of people to this seems to be somewhat different than in English-speaking countries: It's forbidden of course, and you'll fail the test if caught as you might expect, but other students who know about it won't tell you off. English doesn't even have a word for this  and "cheating" definitely sounds harsher.
Some teachers even claim that preparing (but not actually using!) a Spickzettel is a good thing because it makes you think about the subject matter, without which it's impossible to prepare a good Spickzettel. But keep in mind that the Spickzettel was invented before The Other Wiki.
After finishing high school, you generally have two options when choosing how to continue. You may embark on an apprenticeship ("Ausbildung") or you may attend a university (for which you need the Abitur).
An apprenticeship means that you get contracted as an apprentice (Auszubildender, commonly called an "Azubi") by a company and spend the next two to three years alternating between learning the theoretical stuff at a Berufsschule (vocational school) and practical on-the-job training. The apprenticeship finishes with a final exam, but there may be advanced training later on. All German apprenticeships are regulated by the German government, and most apprentices receive a salary. Apprenticeships are considered one of the more successful parts of the German educational system in international comparison.
First of all: In Germany there is no distinction between colleges and universities, and there used to be no distiction between undergraduates and graduates either. The degrees you could get were a Diplom (diploma), a Magister ("master" in Latin), or a Staatsexamen (state exam). Some university still retain these today, but most have changed toward bachelor and master degrees in an attempt to improve their graduates' chances in the international market. This has been a hotly debated issue for the past few years.
The first German universities in the Holy Roman Empire were those of Prague and Vienna. The first ones within Germany's present borders however were Erfurt (1379) and Heidelberg (1385). Now most bigger cities have at least one, along with Fachhochschulen (which have recently begun to style themselves "Universities of Applied Sciences"), and most offer a wide range of subjects from medical science to theology to Assyrian philology.
Note that while most university courses are intended to be finished after three, four, or five years, it seems to be more common than in other countries to stay for six or even seven years if there's something preventing you from finishing in time.
Also note that to obtain a Doctor's degree (PhD) you need to have a master's degree (or a Diplom, Magister, or Staatsexamen) first and have to publish a book-size doctoral thesis which has to contribute to the sum of human knowledge. In addition, in Germany there's no such thing as an MD - any physician who hasn't written a doctoral thesis may technically not call themselves a doctor.
Another hotly debated university-related issue in recent years, apart from the bachelor/master stuff, has been the introduction of tuition payments which also didn't exist before. Each German state deals with this in its own way. Now most states who originally adopted the tuition fees are stopping them again. All of this is still in a bit of flux.
- And we'll leave it there, thank-you-very-much.
- Actually, the school shown here is a Gymnasium with dormitories etc. of its own. The story is set at a time when only bigger towns had a Gymnasium and/or Lyzeum and boarding was the usual way for children from small towns, villages or the landed gentry to attend such schools.
- Actually, we do. It's called "cribbing", and those are cribs or crib sheets, in Japan they're "cunning paper" (this is pretty universal).