Where do I buy characters?

[Josh]

^^^

[darth_biggious]

after finishing the main story either by finding them in the hub worlds (they are marked on the map as the face icon with the studs above), or by bringing up the main character list while in a hub world.

[LeChatMG]

You don't have to finish the story to buy characters, you can either find them in the hub areas (if you chack the map, their icons are a green minifig head with a yellow stud above) or directly buy them from the full character list while freeplaying any level.
Note that some characters are locked in some ways in the hub areas (encased in ice, etc.) and can't be bought directly.