After 15 days they become a teen, and after 30 they become an adult.
It's just a process of time. c:
Or, if you find someone who's willing, they can 'zap' your pet to either teen or adult or back to baby again using a Regression Ray.
Regression Rays are not sold in the Credit Shop at the moment, so you can only get one from another user.
People are quite hesitant about lending them out, though.