The way it works at my school is that we have a pre-med advisor who composes a "committee letter" based on our three letters of recommendation, and he then puts together a packet containing the 3 letters, plus his, and sends it out to whatever medical schools we designate. Unless AMCAS is really different this year, I'm pretty sure they won't be handling letters of rec for you. They only do this with transcripts, so you don't have to have the transcript sent to every school you apply to.
In your case, if you don't have a pre-med advisor who would orchestrate the letter of rec thing, I guess you'll have to give each of your letter writers a list of schools and addresses to send the letters to. If you already know where you're going to be applying, or at least know SOME of the schools, it might be easier to just give them self-addressed, stamped envelopes NOW, and if/when you add other schools you can just call/e-mail them from home and tell them to send the letters to some other places whose name/address you provide.
It's a pain in the a$#, I know. Perhaps one day AMCAS will do the letter stuff for us too, and we could just have our letter writers submit our letters electronically. That would be pretty cool! Anyway, I hope this was helpful. 🙂