There are, I believe 8 or 10 autograph albums, but you are given one by Mickey right at the start of the game. To get a character's autograph, simple wave to interact with them when you are in front of them, then hold your hands out in front of you at waist level, or simply say "Autograph". If you don't have the right album, then you cannot have their autograph, and must purchase the album from one of the many shops throughout the park.
The Sensational Six (consisting of Mickey, Minnie, Donald, Daisy, Goofy and Pluto) autograph album is the first and easiest one to complete, as you are given the album by Mickey and have to get a couple of signatures anyway for the mission to advance. After that, head to Mickey's toontown at the top of the map where the remaining characters are located and obtain each autograph in turn.