As said above, rule number one is do not let their head go underwater. Even a few drops of water may drown a chicken.
You already got one reply, but I'll tell what I know. Get a bucket of water slightly on the warm side to bathe the chicken in. Just be gentle as if you are bathing a baby. Also like a baby, make sure the rooster is never left unsupervised in the water. I use baby shampoo. I don't know if puppy shampoo would work. Get the rooster wet, then add shampoo, then wash. Be careful not to bend or pull on the feathers too much. Afterwards, dry the chicken with first a towel, then a blow dryer (if possible). If you use a blow dryer be careful around the head. Dry from head to tail. Warning: chickens often poop while in or when they're getting out of the water! Set the rooster in the sun to finish drying.
If his feet are dirty you can scrub them with an old toothbrush.
Good luck!