Many people suggest toothpaste, but I have found that it can sometimes leave a visible haze of tiny scratches. Personally, I have used:
1.) Micro-Mesh; you use the abrasive-coated foam pads to remove the bulk of the scratches, moving from coarse to fine. Then you finish with their paste abrasive. The kit is a little expensive, and the process is slow; however, it works VERY well if you follow the directions.
2.) Novus Plastic Polish; this is a paste-based product. You start with the coarsest polish (they call it #3, I believe) and work your way down to the finest one (#2). You finish the job with a thin, milky fluid (#1) that supposedly cleans and protects the surface. Unless the scratch is deep, you can probably start at #2. This product also works well, though it can be a chore to remove all of the fine scratches left by #3. The #1 cleaner DOES seem to leave a temporary protective film (silicone?).
3.) Flitz; I suggest you try this first. It is easy to find and really does work well. It is a great metal polish, too. If you find that it leaves fine scratches, you can always order one of the more expensive products.
To prevent further damage, look at the products sold by Shieldzone. I have used the film on my cell phone and GPS. It is EXPENSIVE, but it does work. Spend the extra time to ensure that there are no small bubbles underneath during application. The instructions claim that these will disappear over time, and they did on my phone but not on my GPS.
-Ben