Locate potential production assistant positions, known in the industry as a PA, by identifying films or TV shows going into production. The Hollywood trade papers, "Variety" or "Hollywood Reporter," run weekly lists of film and TV shows, including addresses and phone numbers. Filmstaff.com lists production crew positions, and sites such as CaliforniaFilmIndustry.com provide lists of production companies that may be hiring.
Contact each production office that is hiring, and express your interest in teh job. Find out the name of the person hiring for that position, because you are more likely to succeed if you can meet or at least speak to him.
Communicate your ability to take initiative and solve problems. A successful PA assists the producer by controlling the chaos that comes with movie making. Emphasize the "local knowledge" you can bring to the job, especially if the film shoot is outside Los Angeles.
Network with other individuals with the same ambition, or better yet, with those already working as PAs. It is likely your job lead will come from a friend or colleague.