I'm in the process of writing a "how to add an image" page as the result of having to answer this question for another user a couple months ago (I should really finish it). Here's what I told them:
Over in the menu along the left edge of every page, there is a link reading "Upload file". (It's actually there twice, once at the top, the sixth item, and once more down under the "tools" submenu.) Click it and it will take you to a page where you can pick the file you want to upload on your computer, add a description, pick a license type, and add categories. (At the very least, include a category for the page the image appears on, and the work it's from, if they're not the same) When uploading an image, please please please provide as much info as you can about the source in the description field, including the original URL and any copyright/ownership information. Here's a good example.
If you got the image off another site, the license will be either "Fair Use", or the license used by that site. In particular, wikis often use Creative Commons licenses, and the license information is usually linked on the bottom of their pages, so you can just go look and see what they use. If you got the image off Wikipedia or from the Wikimedia Commons (like this one), there's a special license selection for that. And if you created the image, there's a special license for allowing your own work on the wiki -- here's an example of that. (What constitutes "created by you" is actually surprisingly broad, as the image at that link might suggest.)
Don't worry about the section that lists what pages link to the image, that's generated automatically by the wiki.
Okay, once you've picked your file and filled in all the blanks, hit the "upload file" button at the very bottom of the page. In a few seconds your file will be up on the wiki. The top of the page will have a banner that reads "File:Name of Your Uploaded File.jpg". Highlight that and copy it.
Then go to the page where you want that image to appear and edit it. Insert a blank line where you want the image to go -- for basically any page, the first image is always at the top, and goes on the second line, under the page type markup. Type two left square brackets, and then past in the filename you just copied from the page you came from. The line will look like
[[File:Name of Your Uploaded File.jpg
If your image is small enough -- no larger than 300 or 400 pixels horizontally -- you can then finish the markup like this:
[[File:Name of Your Uploaded File.jpg|frame]]
That's a vertical bar, the word "frame" and two right square brackets. "frame" puts a border around the image and positions it flush against the right edge of the page, which is where we generally want page images to be.
If it's bigger than 400 pixels horizontally, you're going to want to shrink it. There are a couple ways of doing this; I generally use this markup unless there's a reason not to:
[[File:Name of Your Uploaded File.jpg|thumb|350px]]
Vertical bar, the word "thumb", another vertical bar, "350px", and two right square brackets. This means "put a thumbnail image 350 pixels wide inside a frame and make it flush against the right edge of the page".
Then save the page -- after noting in the edit reason that you've added a page image -- and you're done.