Character Elite Force Trophy

You level you characters in Disney Infinity by collecting Sparks (blue objects found from defeating enemies and breaking objects in the world). You also gather sparks from completing quests in the play sets and winning medals in the Adventures. Completing each of the 3 starter play sets should level that character to somewhere between level 8 and 12 (depending on which play set and how many of the side quests you complete).

The quickest way to level to 15 after this is to select the Castles and Slingshots Adventure and continue getting a gold medal on it until you hit level 15. Thanks to JesseBlur for the tip.

If you have unlocked the fan from the Disney Infinity Vault, you can place it in an empty Toy Box, drive a car over it so that the car is hovering, then tape/rubber band the right stick in a direction to continuously do tricks. This still works for levelling even though sparks do not grant XP in Toy Box mode. Video courtesy of Craig Sullivan:
Note: Currently you do not gain levels from collecting sparks in Toy Box mode so quick levelling there is not an option.