On formal night the characters appear dressed in formal gear and you queue up for a picture. They are usually around at the time of the dinner sittings (and maybe a bit later in the evening as well; I can't quite remember). You usually see Mickey, Minnie, Donald, Chip & Dale etc. My DD15 will remember better than me which characters so I will ask her later.
You don't need an appointment but you do need to be at the line early or be quit patient as the lines can be long unless you time it well.