Depends if you are taking the love or lewd route.
Lewd: You need to buy the higher level outfits available, then unlock them with a reward point (when you are eating with her). The clothing store should say something along the lines of "you could convince her to wear this" - thats the one you need
Love: Whatever love stage you are at should have the appropriate outfits available in the store, just buy and she'll wear them herself
Both need you to do the clothing events that appear once she is wearing an outfit, usually in the kitchen at breakfast, and when she is doing yoga. In order to do the actual leveling up. There's an explanation in the help/tutorial section on the computer with some of the icons and such you need to look out for.