Cats pretty much groom themselves, but there are some ways that you can help your kitty get clean if needed.
The first step to groom a cat, especially if he is new, is to give him a bath. There is much debate over whether cats ever need baths at all. In my opinion, they need baths once in a blue moon. Bring him into the bathroom and lock the door. Your cat will probably start to look at you out of the corner of his eyes at this point, so you’ve got to act quickly. Put a bottle of cat shampoo on the tub and turn on the water. Put kitty in the tub and slowly wet him with your shower nozzle. If he doesn’t like it, just put a little bowl of water next to him in the tub and cup water over him. Soap him up, rinse him off, and then wrap him up in a snuggly warm towel (they love this part).