Tag-Along Actor

An actor for a Show Within a Show researches the role of a special profession by shadowing his Real Life counterpart. The counterpart is often annoyed at the presence of the actor, whom he feels is getting in the way of his work. Expect This Is Reality Lampshading when the shadow realizes that the real job isn't like it is in the movies. Sometimes ends with a promise to change the movie's script to better reflect reality.

Less frequently, the shadow is a writer or a director.

This is a common stock plot on cop shows, where the usual course of action involves the actor overstepping their bounds as an observer, then learning a lesson about how law enforcement is a hard job and shouldn't be attempted by someone who doesn't know what he's doing.

Film

 * The Hard Way: An action movie from 1991 starring Michael J Fox and James Woods, in which an action movie star shadows a police detective for research so he will be taken more seriously as an actor.
 * Into The Sun, starring Micheal Pare and Anthony Micheal Hall, had a Hollywood actor shadowing a fighter pilot stationed in the Middle East to "get a feel" for being a fighter pilot. The actor gets to learn far more than he planned to when the plane he is riding with the fighter pilot in unexpectedly gets into a dogfight and is shot down, forcing the two to help each other survive and escape.
 * In My Favorite Year there's a movie actor who prepares for his roles by imitating real people. In one scene he's sitting in on a discussion between a Mafia don and some movie exec, and the don is getting irritated by the actor constantly imitating his mannerisms.
 * Showtime, starring Eddie Murphy and Robert De Niro. This one put a slight twist on it as Eddie Murphy's character was a cop, but was more interested in launching an acting career, while De Niro's character was frustrated that Murphy did not take his police duties seriously
 * Southland Tales has action star Boxer researching the role of a racist cop by riding along with Taverner (who is actually pretending to be both racist and a cop).
 * In Tropic Thunder, extreme method actor Kirk Lazarus mentions at one point having prepped for his third Oscar winning role by working in a Beijing textile factory for 8 months.

Literature

 * In Help! I'm Trapped in a Movie Star's Body, the eponymous movie star tags along after the Ordinary High School Student protagonist.
 * In "Out of the Night When the Full Moon Is Bright" by Kim Newman, the protagonist is a writer who's riding along in an LAPD squad car as research for a screenplay. (The usual course of the stock plot, however, gets derailed after a werewolf shows up.)

Live Action Television

 * The entire premise of Castle, in which mystery writer Richard Castle, author of the Nikki Heat series, follows Detective Kate Beckett around at her job in the NYPD.
 * Also features in the episode "Nikki Heat," where Natalie Rhodes, who will play Nikki in the movie adaptation, shadows Beckett for a case as well.
 * An episode of Martial Law had this. Interestingly despite the show being a Cliché Storm it more or less deconstructed this trope, with the actor being admonished for doing something heroic (intervening to save them, since he was a civilian) and gets lectured again when he has a break down and goes on an I Am Not Spock rant at the victim of the week.
 * One episode of Midsomer Murders had an actor boyfriend of Cully's riding along with Barnaby and Jones to research the role of a detective sergeant. It's a comment of his that gives Barnaby the Eureka Moment.
 * In Monk the titular detective had also an actor following him around.
 * On News Radio James Caan meets with Bill to research for a role as a newscaster. Bill tries too hard to suck up to him, while Caan becomes increasingly fascinated with Matthew instead.
 * The Sledge Hammer episode Hammer gets Nailed had Hammer and Dori being followed not by an actor but by a TV reporter for research.
 * Tequila And Bonetti had one episode with that premise.
 * The X Files episode "Hollywood A.D." did this with a movie director instead of actors following Mulder and Scully on an investigation.
 * Forever Knight: In "Amateur Night," an actress shadows police detectives Nick and Schanke to research for a movie role. She ends up getting too involved in the case, putting herself and others in danger. In a humorous parallel, Schanke learns more about the movie business and decides he wants to purse an acting career.
 * Sue Thomas FB Eye: In the two-parter "The Actor" and "Planes, Trains & Automobiles," the movie star Adam Kinsey shadows FBI agents as they investigate a possible terrorist threat. He constantly questions their actions, and the one time they agree to his request (cuffing a suspect's hands in front rather than behind her back) it ends badly (she is now able to take poison and kill herself). Reinforces the show's usual Aesop about how law enforcement knows best and is doing the right thing, even if their reasoning is not readily apparent to an outsider.
 * CSI "I Like To Watch" had a TV crew following the CS Is. It even made a joke about the actual show, something about "beatiful people solving crimes" being a good idea for a show.

Western Animation

 * The Simpsons:
 * In one episode, James Woods researches the job of a Kwik-E-Mart employee as a reference to The Hard Way.
 * Another episode had Mr. Burns hire Michael Caine to impersonate Homer in order to convince Bart that he (Homer) didn't love him (Bart) any more. Later in the episode Homer mentions that Caine had followed him around trying to get a handle on his character.
 * Archer: A Hollywood actress who is going to be playing a spy tags along with ISIS agents to get into character.

Real Life

 * Dustin Hoffman spent a year working with autistic men and their families to understand their complex relationships as a preparation for his role in Rain Man.
 * For the Film Ray Jamie Foxx studied Ray Charles to better mimic him. After a few weeks he stopped visiting Ray saying that a 73-year-old Ray Charles couldn't help him in portraying a 19-year-old Ray Charles, up until age 49, by the movie's ending.