No appointments are necessary. Some people arrange to have a special time with a photographer and for that you'd need an appointment. Other than that the photo ops are first-come first served, line up and wait your turn situations. Each character will have a ship's photographer with him/her and there will be opportunities each night to have your photo taken with different backdrops. they also do something called Lifestyle Portraits. They are done on Deck 3 in the Atrium and have a white background. The photographer will take 10-15 shots of your family, including any subsets (just the kids, girls-only, etc.) that you want. These happen at certain times. No appointment is necessary, you just line up and wait your turn.
All photos will be posted in Shutters on Deck 4 Midship. You go there, find your shots and decide which ones you want. You can try to stack them until the end of the cruise and make your decision then, or you can purchase a package up front. If you get a package and don't use it all or need a bigger one they will let you adjust it. They will also let you switch out photos for ones you like later in the week so we've never felt the need to stack our shots. We buy the smallest package and select as we go, trading out or upgrading the package later in the cruise if necessary.