When you do something in a way that expresses your displeasure, you act disapprovingly. You'll know that your teacher isn't buying your excuse for being late when she starts frowning and shaking her head disapprovingly.
If you're a fan of fireworks, you approve of them, but if you think they're noisy and wasteful, you disapprove. If you let this disapproval show, you're acting disapprovingly. When your mom disapprovingly asks your friends not to eat in the living room, she makes it clear she's not in favor of crumbs in the couch. And if you comment disapprovingly on an online news story, you're likely to get equally cranky responses from other readers.