Mild to moderate yellowing and light scratches can be polished out with a one-step process using Meguiars Plast-X polish and a terry cloth or wool bonnet. I use terry cloth and a 6" random orbit buffer.
Only wet sand if absolutely necessary.
New UV coat is trickier. There are a lot of off-the-shelf options and as many opinions. Most consumer products are very temporary and will need to be re-applied every month or two, depending on how much sun your car sees. The best UV coats require sanding the old finish off completely and use of a UV cure light (which I don't even have).
That's really best left to a pro. I've only had limited success with complete restoration and only on my personal headlights.
I generally stick to polish and it does make a significant difference.