I was on a forum the other day where a cat owner posted a photo of her arm. She had recently been on the receiving end of the paws of fury and her skin showed the battle wounds of having business with an angry cat. Her post contained the details of that battle - a bath.
The community was up in arms (pun only slightly intended). Apparently, some people do not understand that there actually times when it is not only necessary to give a cat a bath, sometimes it is absolutely vital and confuse caring for a cat with torturing a cat..
There are a few things to keep in mind when you find yourself in a place where you need to give a cat or kitten a bath. You need to remember that cats have a higher body temperature than we do, so having water that is warm to the touch is important. If you can, keep the room warm as well, this will also help the kitty stay nice and warm. Kittens more so as they have a very hard time maintaining their body temperature. You want to use as little soap as possible to make bath time a bit easier; the more soap you use, the longer it is going to take to rinse out.
You will understand the importance of knowing that sometimes bathing a cat is a good thing, when you find yourself with an adult cat that, oh say, investigated a bucket of heating oil (that stinks to high heaven) by sticking her feet in it and then shows up in your bed in the middle of the night to tell you of her adventures.
I find it helps if you have a milk crate or a very sturdy laundry basket that you can put into the tub upside down to give the cat some place out of the water to stand while you soap up the important parts. I will fill the tub up with several inches of warm water, put the crate in the tub, get a large cup that holds 16+ oz of water and then get the cat. I place the cat on the crate with its face pointing away from the exit.. either into the wall or into the corner. Once I'm in position, I will take the cat off the crate and put it into the water. The cat will want to escape, but keep redirecting it towards the wall, do not let it turn around or it will see the exit and fight to leave.
When I bathe adult cats, that first initial contact with water is generally the only time the cat is submerged in water. This is the fastest way to get most of the fur wet. When I am comfortable that the area I need to clean is soaked, I let the cat back up on the crate and get the soap. Using as little soap as possible, I lather the area to help loosen the dirt (or oil, or whatever). I then use the cup to scoop up the tub water and gently pour it on the cat to rinse away the soap and debris. This can take some time and chances the cat has long since given up on dealing with your shenanigans and really wants to leave. Just keep redirecting the cat over and over toward the wall. If your cat is a bit like a Gremlin when it gets wet, you might want to think about investing in a muzzle, which covers the cat's eyes so it can not see to escape and keeps the mouth closed. This will not protect you from flailing claws, but hopefully, you trimmed those before you started.
Once you are satisfied that the bath is successful, Getting your cat into a nice big absorbent towel will help minimize the distribution of water around your house. Wrapping the cat up will hopefully provide a little security to your cat that the bath is over. Your cat might be so over your shenanigans that it wants nothing to do with you and wants to run off and lick itself to restore some semblance of normalcy in scent and demeanor. If your adult cat is in good health, allowing it to run and hide is generally okay and will not result in the cat becoming too chilled. Checking on it in a few minutes, offering treats as a bribe will help reassure you that all is fine.
Young kittens and cats that aren't in the best of health need to monitored to ensure they do not become too cold.
I've found that kittens do not want to be snuggled up into a towel, so I will pat them dry, then let them down for a few minutes. They will start to groom themselves to "fix" what I've just done. When they become distracted from grooming - which inevitably happens - I will scoop them back up into a towel and work on drying them and warming them up until they struggle to get down. I'll do this over and over until they are distracted by food and start to eat.
So, yes, you should give a cat a bath if you have a reason to do so. You should keep the kitty as warm as possible while doing it and monitor them until they are completely or at least mostly dry.