I have some black plastic parts on the outside of my car that need cleaning.
You can just use normal car sop which has some sort of wax included with it, and if you want it to shine, you can get like a leather polisher (for cars) and almost paste it on and let it dry, you can also use that leather polisher for your tyres and interiour. Some also have nice scents :D
i use something like armor all.
You can use soap and water but you can also use a cleaner because the plastic will not absorb any liquids.
On my 86 Vette there's a black plastic piece which goes around the mid point of the car. While soap and water is normally how you'd clean it, it's a pain if wax gets on the plastic, as it turns it white. Soap and water doesn't remove the wax. So I bought a product called Back to Black at my local auto store. You just use a soft cloth and buff this into the plastic and it removes the wax, and cleans the plastic to like new. Give it a try, it's cheap.