As you can see below, they put their dirty dishes and cups into the replicator which then reverses the replication process (to allow the material to be used later);

From DS9 : Hard Time

KEIKO : Make sure to put your plate in the replicator. MOLLY : Okay. Molly picks up her plate and puts it in the replicator. It disappears...

and DS9 : The Ascent

SISKO : I'm afraid Jake's going through a phase of his own. (a beat) I don't know what's so difficult about putting a dirty plate back in the replicator.

There's also a note in the Star Trek TNG: Technical Manual that some replicated materials (water and clothing) are recovered through mechanical and chemical means whereas food is most often returned to the feedstock pile due to limits on resupplies while in space: