When you're actually playing through the game the first time, you have to use the PROPER characters for a scene. I.e. if you're in a scene with a troll and it's supposed to be Harry and Ron facing against the troll, that's what you do. However when you finish the level and can go back in "free play" mode, you can be whatever characters you want! The way you get other characters is a two part process.

First, you have to "unlock" each character. You do that by performing some sort of action in the game. So for example saving a boy from a tall bookcase might unlock that boy's character for you to use. You will see a small circular face of that boy appear on the screen and a message will indicate that you've unlocked him.

Second, once the character is unlocked, you have to choose to BUY that character for your roster. You do that in the dress shop. I have to say the interface for choosing characters is AWFUL. You have to cycle through portraits one at a time and since they mostly start out "locked" it is really hard to scan for the ones you do have available to buy!!

Here are the characters you unlock, and how you do it.

Ron - in dorm room, in chest
Griffindor Boy - in dorm common room
Boy - saving the boy in the levitation classroom
Girl - zap all four candlesticks in the lumos classroom
Gryffindor Girl - after the Lumos class, in the main hall, chase the girl with the token in her hands into the snake

Padma Patil - raise all the banners (set 1) before the Quidditch game
Katie Bell - raise all the banners (set 2) before the Quidditch game
Ravenclaw Boy - burn down the food stand before the Quidditch game
Harry Tuxedo - go into the dress shop area

Lego Harry Potter Walkthrough