Depends on your interpretation of "dirty", if you mean "pervert", you could say 色狼, but that tends to be reserved for males. If you just mean that someone sleeps around a lot, you could describe them as 好色 (here 好 is an active verb meaning "to like"). 好色 tends to be reserved for men, although I think I've heard it used for women. If you mean a sort of "temptress",for females, you could say 妖精, or if you wanted to be more vulgar, 骚货 (loose woman).
Keep in mind these can all be fairly offensive, even when used jokingly. 好色 is probably the least offensive.
Those are all the things I could come up with off the top of my head. I'm sure some native speakers have better terms.
Razzle told almost everything,but still I have something to say
If I want to translate the "dirty person" you mean,I'd say 采花贼 or 沾花惹草的人.But they're usually for man.
More humorous,we can say "you are a 西门庆" to a "dirty man",西门庆 is a character in one of the most famous Chinese classical novels,《水浒传》(Water Margin),he is so typical that he becomes a specfic call for men of that kind.
For woman,we have 荡妇,娼妇 or 浪荡的女人,they're even more offensive than what Razzle have said.
As for "她很黑",I think I heard this before,but I think it's 她很腹黑 and 她黑化了 which don't have nothing really to do with "dirty" things.
the word 黑 is popular and colourful in meaning nowadays,it may refer to "dirty" or stuff if there's a context.
In a certain context, we may say '他/她很亂' to imply that a man or woman has a messy sexual relationships with many people, or you can just say '他/她私生活很亂' to describe that he or she has a lot of sex with different people in personal life. The sayings above are quite scandalous.
These sayings are what I hear in Taiwan, especially among young people. I'm sure there are other terms used in other Chinese-speaking region :^)