There are more than a few posts on this subject for you to research so you can make up your own mind. I will not give an in-depth answer, but will make a couple suggestions.
1 Choose someone whose work / talent etc that you admire.
2 write a polite and respectful letter (LOR).
3. Be sincere. I am an eclectic collector and have a large and varied collection but still treat every request as if it is special (and it is!) sincerity helps gets positive results.
There is a lot more to be said, but I repeat, there is a lot of information on this site to help you get started. Finally just check the feedback section and see if some one that you are a fan of has signed for someone else, then take the chance and write to him/her.

I just founf this website today and I'd never really thought of autograph collecting before, but it seems like a lot of fun. I have absolutely no idea what to do though...I mean, what exactly should I write in a letter? How do I know it's an authentic autograph? I need all the help I can get. Thanks everyone!