Acrylic is a versatile plastic that can be heat formed, vacuum formed, machined, and used easily with just about any shop tool. It can also be sanded: but once you sand it, you lose that nice clear surface finish. It's easy enough to get that back with a small butane torch.
Step 1: Step One: Fill Your Torch
This is the fuel and the torch posing for the camera, but you're going to want to fill the torch upside down. Don't overfill: less than a second is usually enough.
Step 2: Step 2: Polish
Get set up in a space that's well ventilated, free of distraction and flammable material. Acrylic can catch on fire, so be prepared with a functioning extinguisher just in case things do not go according to plan.
Hold the torch at a low angle across the material. You want to heat the surface, not the whole thickness of the plastic. Move the torch continuously as if you were painting: you want the plastic to reach the temperature just before flame up, but not actually catch on fire. As soon as you see the surface turn shiny (or just before), you'll want to move the torch away: lingering too long will cause it to flame. That'll ruin your surface. If a small flame does occur, you can blow it out right away. Don't push the boundaries though: this is plastic, on fire, so if things get too hot, put safety before your project.
If a small flame does occur and you blow it out, you'll notice a the surface will look roughed up and distressed. Let it cool off, completely, and hit it again with the torch, being extra careful to move on at the right time. If at all possible, you should never torch the same area twice. Though acrylic is somewhat forgiving, you don't really get do-overs!
Have fun, and be safe!