Look for bright yellow signs with black lettering and arrows to find shooting locations for movies and television shows. You might not be able to get too close to the actual scene, but you could catch a glimpse of the stars going to and from the set.
Hang out by restaurants and stores near movie and television studios. Television stars in particular get used to going to certain spots around studios, since TV shows have longer taping schedules than movies. While most studios are in Los Angeles, Universal Studios is in Universal City, Sony is in Culver City and NBC, ABC, Disney and Warner Brothers are in Burbank.
Buy a star map from one of the many peddlers in Hollywood. They are often out of date, and the celebrities might not be of the stature you want.
Take a tour of the city that targets stars' homes, like the ones offered by Starline Tours. They are more up-to-date than star maps, but don't expect too much. Many houses are either far away from the street, or they're hidden behind walls, fences or bushes.
Attend a Los Angeles Lakers or Los Angeles Clippers basketball game at the Staples Center. As of this writing, Lakers regulars included Jack Nicholson, Denzel Washington, Leonardo DiCaprio and Dyan Cannon, while Billy Crystal, Penny Marshall and Frankie Muniz often go to Clippers games. You probably won't be able to sit too close to the celebrities, though; they usually buy seats near the court, which can cost over $2,000.
Get a schedule of red-carpet or special events involving celebrities. Many of them take place at Grauman's Chinese Theater or the Kodak Theatre on Hollywood Boulevard.
Be part of a studio audience at the taping of a television show. Network websites have contact information for their ticket offices. Some show tapings can last up to four hours.
Go to a comedy club like The Laugh Factory or the Comedy Store. As of 2011, big names like Dave Chappelle and Dane Cook still "dropped by" the Los Angeles clubs to work on new material.