How should I feed a cat?
I found the answer myself. In Ados City, NPC Felina sells cat. She tells you how to feed it as well.
Cats love chicken and fish. Just place a piece on the ground and your cat will run over to eat it. You can right-click on her and choose 'Look' at any time, to check up on her weight; she will gain one unit of weight for every piece of chicken she eats.