The best way to do that is to remove the trim piece from the car and use a small buffer ball. Polishing plastic by hand can leave mixed results. As for polish, I like Optimum's Polish for plastics.
This is where it helps to have someone remember where the heck the thread is that already covers this topic to death and has GREAT before and after pictures.
The OP for the above thread hosted his pictures on Photobucket but I downloaded them and then uploaded them to our gallery so they wouldn't disappear...