I’m not even going to ask how that happened… but I have three great solutions nonetheless:
Most paints you’ll have around your house will be water-based, by thins I mean, the emulsion paint for your walls, some gloss paint (these can be both oil-based and water-based), the kids finger-paints… grannie’s watercolour set. Now these paints are generally non-toxic and mostly harmless, but you wouldn’t want to eat them, so it’s a great idea to bathe your cat, before it decides to groom itself and lick all the paint off. The water and cat shampoo should do all of the hard work and a quick but thorough brushing should sort the problem out easily enough.
Now I’m just guessing, but I doubt your cat just ran past Picasso in mid-surrealist-stroke, So oil-based paint is more likely to be your big industrial nasty, it’s a nightmare to get out of anything, Also, if you can paint the hull of a ship with it, you definitely don’t want to eat it. So this is a great, natural way to remove oil based paints, as I assume you already know dousing your cat with traditional paint thinners is probably going to be worse than the paint itself. Instead rub vegetable oil into the affected area to lift the paint and then wash your cat thoroughly to remove the vegetable oil and paint. Once again give your cat a good brushing to make sure it’s all removed.
If the worst has come to the worst, your cat is covered in paint which has dried and matted in. With water-based paints, this should still come out just with water and cat shampoo, with oil-based paints, you only really have one option, and that is to cut it out. This might be a good option if your cat gets all snarly at the sight of water too. I doubt you need further instructions, but just in case… you get the scissors between your thumb and forefinger… and… lol just kidding… your cat will look a bit stupid until the hair grows back but c’est la vie.