Tell me about frequent flier miles

[JTG51]

I haven't really flown enough (or at least not paid for the tickets often enough) to think about frequent flier miles before. Now that I'm on the West coast and my family and friends are on the East coast, I think I should look into it.

I just got a credit card application in the mail with some kind of frequent flier miles program. It says I get 15,000 miles for signing up, and 1 mile for every $1 that I charge. That sounds great, but it doesn't say anywhere on the paperwork what each mile is worth. Does it take 1,000,000,000,000 miles to fly from coast to coast?

Can someone tell me what a typical plan is? Are all of the plans similar? Is it worth shopping around?

Thanks.