If the kitten has been wee-ed and feed-ed and isn't a mess, then I ususually wipe him down with a warm slightly damp wash cloth. And because you could patch concrete with the kitten formula that dries around the kitten's mouth, while it's still damp I comb it out with a extra fine flea comb. After I use the comb, I use the warm, moist cloth to go the face, then front paws, tummy, back legs and the poopy area (in that order). Make sure the room is warm so he doesn't get chilled.
If you have a kitten who's peed or pooped on himself, or if you have an active litter that have been stimulating each other (and are covered in poop) *sigh* it's time for a real bath. Make sure the water is nice and warm. I use a digital temp meter to tell me it's in the 90s. I also use either a baby shampoo or a tearless cat shampoo. It used to scare me to death to have to bathe them. But you have to wash them because you don't want them getting ammonia scalds.
When you bathe a kitten, you must keep the room in the 90s (I use an electric heater to make sure the room is warm enough.) The water should be in the 90s. Wash fast, dry thoroughly. Use a blow dryer on low heat to dry him off. A hot dryer will badly burn that delicate skin.
Bathing a kitten only takes a few minutes. It's when you have an entire litter of poop-covered kittens that it takes a while. And when the litter has coccidia, you may have to hit the showers three or four times a day.
Learn from my mistakes. Never leave a drying kitten alone. One time I left a damp kitten in a room with the electric heater. When I got back she'd almost passed out from the heat. I put her in a cool damp cloth and she was fine. But if I had been distract much longer, I'm sure I would have lost her.
Never let the kitten get chilled. Cold is the great kitten killer. Last year I picked up a litter of two week old kittens from animal control. The week before I had shown the girl in the kennel how to wee them (sometimes it's almost 24 hours before a rescue can go pick up the orphans so I wanted her to know how to care for them.) When I arrived, someone brought me two tiny babies wet to the bone with almost no body heat. The girl had pooped them and then hosed them off cuz they got messy. She never even towel dried them. I tried to warm them up but they had gone into shock. Their kidney's had already shut down. It broke my heart. Stupid me. I assumed this young girl would know how important warmth was.
You won't have a problem if you work quickly and keep him warm.
Another tip is while the kitten is being bathed, have a few towels cycling in the dryer. Have someone else retrieve the towels (they must be clean towels, dry and the dryer set on low). Use one towel to dry the kitten, and one to wrap it up keeping an airway for it near the head. Sit down in a comfortable chair and hold it close to your heart and snuggle with it until it is dry.
Don't go to the trouble of giving a body bath when a butt bath will do. If you have poopy legs and tail, you can give a bottom bath under running water. Don't forget to use shampoo to wash out all of the ammonia and rinse him well.
Butt baths don't take as long, and they're faster to dry. It's a lot easier when you have to cope with an entire litter poopy kitties.
You can also warm the towels on a heating pad and pull them off the pad to dry them. Saves having someone shag the towels out of the dryer for you and works if you are alone!
I keep my washclothes in a bowl of very warm water nearby. Rinse them out, make sure they are neither too hot nor cold before using them on the kittens. If one gets messy, you can pull a second one out without having to leave the room.