Be friendly and polite. No one is going to finish reading a letter that starts out, "You @#$%, give me what I want or else!"
Use correct grammar, spelling, and punctuation. We tend to be sloppy about those things on the net, but to the rest of the world, they are very important. We want to come across as being reasonably mature, well-educated, and professional - the kind of viewers networks want.
Be brief and to the point. These people are busy, and keeping your message concise shows that you value their time and attention.
Write a letter, not an e-mail. Snail-mail has more impact than e-mail, since corporations tend to be old-fashioned. And they don't think Internet fans are normal viewers. Use a business-size envelope and type rather than hand-write the address on it.
Get your friends to write, too, but please, do not spam. They won't be impressed with a bunch of identical, photocopied letters or a lot of signatures on one letter. It's better for each person to write his or her own, original letter.
Write them more than once, but again, do not spam. Send them a message once every week or two, just to let them know you are still interested. And sign your real, full name.