Use Plexus, its a cleaner plus plastic polish, works well with Chromed Plastic. Removes bugs pretty fast too - http://www.plexusplasticcleaner.com/plexus.html
I have had good results with Klasse All-In-One Polish Not only is it good with (plastic) chrome, but it is very good in polishing virtually any car body parts, including the plastic headlights. It truly is an all-in-one polish.
Some straight forward chrome polish should do the trick. And it will only cost about $5.
Use Plexus, its a cleaner plus plastic polish, works well with Chromed Plastic. Removes bugs pretty fast too - http://www.plexusplasticcleaner.com/plexus.html
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Depends on what needs to be cleaned off. I use one of these to clean the front of my car (for bugs, etc)
Bug Sponge
As for polishing the plastic, there are some products from Mothers and Meguiars that can be used.
I have used the polish from Mother's before: Mothers Plastic Polish
If you have to remove yellowing or other deterioration/discoloring you will need a buffing wheel to get the results you are looking for. There are some buffing attachments that can be used on a power drill and if the trim is big enough you can use something like that but you have to be careful about how much pressure you apply as you can burn the plastic. You can also tape off areas about the piece you are buffering with tape from 3M
That tape is awesome, protects and will not hurt the paint, etc.