Buffing out scratches on acrylic tank?

How bad are the scratches? Are they able to be grabbed with a fingernail? If so then your going to need some various grades of wet dry sand paper.

Start off with about 220 grit. Sand only in one direction. Then go up the scale from 220 to 320, 400, 600, 1000, 1800 or 2000, 3200 and then polish. The polish is made by Novus.
Be sure to NOT do circular motions and Make sure each time you switch grade of paper you switch direction across the previous.

If the scratches are less then that you can start with a much finer grade.

On some stuff the novus may be enough. I like to use the novus with a polishing pad and a buffer. BUT BE VERY CARFUL. you can actually burn the acrylic.

^This, and make sure to clean the acrylic in between sanding with a different towel for each grit. If you use the same towel it will track dust from the bigger grits and you'll have to start over. If you can't find novus there's a product I use called Meguiar's PlastX and can be found at walmart or any store that sells car cleaner. You can also find a buffing kit there made by Turtle wax that comes with pads that attach to a hand drill and works great. I've also heard that micro mesh works better than wet/dry sandpaper and comes in kits specifically for aquarium use. It's a little more expensive but I'm thinking about using it on my 240

The sand paper method works great and there is no compounds to pollute. I use wet sand paper and water to keep rinsing the paper, The do wipe between grits of sand paper. I actually did this with a kit from fosters and smith, With the fish in the tank. I just lowered the water and floated paper towels to catch the debris.

I'd use Novus and a buffer pad attached to a drill to get out the scratches. You can find it on amazon. Buy the bigger bottles because you always end up needing more than you think. If its too scratched up though there might be no saving it. If there are too many long, deep scratches visible even when you have the tank full of water then I would pass on that tank. Most every used acrylic tank looks scratched up when it's empty but it's how it looks when it's filled up that's the key imo.

3M also makes a platic polish kit (get it at a car parts store - for headlight restoration). I like Novus the best, but the 3M works well, too. I used it to take out some major stratches on the shark tank (both dry and underwater).