Rust-O-Leum (sp.?) and Armor All both have a “Two Step” kit that works remarkably well.
It is very simple to use — clean (scrub) the headlight covers with the first cleaning/polishing wipe, then use the second “finishing wipe” to ‘fix’ the shine onto the plastic covers.
Both kits run about $12 at Advance Auto or O’Reilly’s outlets, although I imagine that Amazon/Walmart/etc., may have them for less.
All the best!