General bathing: Keep in mind this is basics; if you have a longhair I'll add comments at the end for a few extra steps.
1. Trim all cat's nails and clean eyes and ears first. Comb cat and be sure there are NO mats or tangles in the coat.
2. Before taking the cat in the bathroom and closing the door, run about 2 inches of water in the tub - make sure its a little warmer then warm but not too hot either. Have two towels ready (warm then in the dryer first). Have shampoo ready on the side of the tub.
Its easier to rinse if you have a hand held shower head attachment; otherwise you will need a cup for pouring water over and over the cat in the end.
3. Gently place cat in the tub and face them to the back of the tub. They may try to get out at first, but talk gently to them and hold them down in the tub. Do NOT get water on the cat above the neck. You might need two people (one to hold, one to do the rest). Use a washcloth to get the cat wet and flip the coat back to wet to the skin. Cat should only be washed from neck down with shampoo. If he wants to stand in the tub on two back feet and hang on with front paws, its ok - let him - easier to wash and rinse.
4. Don't use too much shampoo as it will take you longer to rinse. Wash neck, chest, body, tummy, legs, and tail with shampoo. Work it in good and then use the washcloth to help get most of the shampoo out. Empty the tub so there is no water the cat is standing in. Now the tricky part (rinsing).
5. Rinse the cat using the shower head but be careful you do not spray in the face, head or ears. Keep your hands close to the body to be sure the water is not too hot or cold. Rinse, rinse, rinse and then rinse again. You want to be sure all shampoo is out of the coat everywhere. Do NOT use gloves - you cannot feel the coat to be sure its squeaky clean and no shampoo left.
6. After rinsing then kinda "squeeze" the water out of the coat, running your hands down the body, legs, tail, belly.
7. Wrap the cat in the first towel and start rubbing the cat dry on the face, chest, feet, belly. Then sit the cat on the floor and rough dry the body and coat and tail. Get as much off as you can. Use the 2nd towel to continue drying by hand.
8. Smooth out the coat and put the cat in a room with no fan, open window or drafts. Usually will take and hour or two to air dry and for the cat to lick himself dry. Don't let the cat out till most all the fur is pretty dry to the touch. You can comb the cat after totally dry to be sure the coat is laying flat.
Now for longhairs, you will need to use a blow dryer for drying. I always thought we were to comb and blow dry the longhair so it doesn't tangle, but the longhair cat showers said to air dry for a little while and then start combing when the coat is damp. They can add to the extra steps for a longhair bath/grooming/show tips.