Finish new buildings to unlock new characters! You'll discover new buildings as you complete quests for the characters you already have. But keep in mind: before they’ll join Peter in his Epic Quest To Fix Something He Definitely Did Not Cause, you first need to make it worth their while. Or solve their problems. Basically, you have to give them lots of stuff. This is called a dilemma. 

To get a character to join you, tap on them to see what they need. You’ll get this “stuff” by performing actions with other characters. For instance, make Peter dance his pants off in order to get a nice fetching pair of pants.

When you've received enough items for the character, tap the dilemma bubble again to hand them over. When you’re done, hit the checkmark that appears.

You can also unlock instantly by hitting the instant finish unlock button.