Join the fan clubs of your favorite actors and actresses. Many times you will receive a welcome packet in the mail that will include an autographed photograph of the star. If you don't receive a photograph upon joining the fan club, you might receive one during the course of your membership, to thank you for supporting the celebrity.
Write the actor a letter. You can get their contact information for their talent agency or public relations firm from their website. Many celebrities respond to fan mail or at the least, have a staff that responds to fan mail. There's a good chance they might send you an autographed photograph of the celebrity to thank you for your letter.
Purchase an autographed photograph of your favorite actor or actress online. Make sure it comes with a certificate of authenticity to ensure it is legitimate.
Read the news, check the celebrity gossip blogs, and look for updates on their websites about where they have been spotted lately. You mind find that an actor is shooting a movie on location in your town, which could enable you to get an autographed picture firsthand.