Here's what you will need:
Large (8.5 / 11) Envelopes
Item You would like to have signed
Step 1: Find Address you'd like to send to
I like to use Fanmail.Biz, they have a very large database, and a forum for posting successes and/or failures.
Look up your celebrity, and see if people have had successes from them before, and from what address.
For this example, I chose actor Aaron Eckhart, of 'The Dark Knight' fame.
If your interested, I used this address:
c/o Hirsch Wallerstein Hayum Matlof Fishman Llp
10100 Santa Monica Boulevard
Los Angeles, CA 90067
Step 2: Fill out envelope to celeb
I will say that you should use a minimum of three stamps on this envelope.
Step 3: Fill out a SASE
Remember, these guys are doing a favor for you by signing your photos.
Two stamps should be fine.
Step 4: Write a letter of request
Step 5: Package and mail
Stick in mailbox or drop off at post office.
Step 6: Wait.
I'd suggest finding a productive way of occupying your time. Learning a new language perhaps.