Sign up for a pro membership at IMDb.com. For a monthly fee of $12.95 or the discounted yearly fee of $99.95 (2009 prices), this site gives you access to a myriad of celebrity agent, manager, and production company addresses and phone numbers. Send your fan mail or professional querry letters to any one of the listed addresses. Your mail will be screened, but with so many address options it has a decent chance of reaching the actor.
Try Facebook or MySpace. Many celebrities now host fan pages as well as personal pages on these popular networking sites. A few actor's pages allow you to send a message directly to their inbox. If there is no messaging option, you can at the very least post something in the comment section, which can be read by the general public. The comment section also can serve as way of asking other fans for help in contacting the actor.
Post a classified ad in the trade papers in New York and Los Angeles if you are looking for actors to do a reading of your screen or stage play (see Resources) Many actors looking for work and experience will be willing to do a read through for very little salary. Try posting the same ad on Craigslist as well.
Enlist the help of friends and family. As they often say in show business, "It's all about who you know." Networking is a huge part of an actor's life in both Hollywood and New York. Often times you can get actor friends or friends of friends to do a read through for free. You can also offer to trade services. See Resources for a link to a DVD movie about how by networking one average Joe was able to contact and have a date with Drew Barrymore.
Be tenacious. Finding a famous actor can definitely take time and hard work, but it is possible. Finding unknown actors to help you with a project is of course easier, but will also require patience if you plan to audition them until you have found the right actor for your needs. Never stop networking and hang in there.