i'd start with Adams APC to clean it. Spray it on, let it sit (out of direct sunlight. you don't want it io dry on the plastic) then agitate and wash off. follow up with a protectant. There's lots of stuff on the market for protecting plastic auto pieces these days. The Griots or Adams VRT is a good water based protectant. I've been using Adams VRT for 10 years, on my tires, vinyl flares, and rub strips. I like the satin finish it leaves vs. the shiney armor all crap.
if you want something that lasts a little longer, you can try CarPro Perl