Normally, your school's pre-professional committee will receive them and package them in some way. The pre-proff committee will either combine the different letters into a single summary letter, write its own letter while attaching your other letters, or simply pass on the letters to AMCAS exactly as it receives them.
If you do not have access to a pre-professional committee, then you can get the letters yourself and mail them to AMCAS, or have each letter-writing professors mail in his or her own letter.
I believe the schools prefer blind LORs, meaning you have not seen them, because theoretically the professors writing them know that you won't see them so they are more open and honest about you. (I may be wrong about this blind LOR preference though) Something to consider though. . .