There are a lot of things that you can find out about an auto body shop. Almost all shops do painting, body repair, and some engine repair. This means if your car has damage due to an accident or needs to be rebuilt they can fix it. Most will also repaint your car if you want a simple color change or some highlighting.
Almost all shops will be happy to give you an estimate for painting or body repair. If you are looking for a body shop there are a few things that you need to look at before choosing. The first is if the shop itself is clean. The second is whether or not they show their previous work. The third is whether or not your insurance company or other insurance companies use them.
It might not seem important whether or not the shop is clean considering what they do there. It is extremely important because especially if they are painting your car. Things like dust, hair, and metal shavings can get into the paint while it is wet. Some can be fixed but a lot of it cannot. Make sure at least the paint booth is clean before having your car painted there.
A lot of body shops will let you look at work conditions. If they do not you might not want to choose them. It is usually a good sign of a good body shop when their shop is neat and clean. Their might be some dust if they are currently working but for the most part it should look good.
When insurance pays for a body repair due to an accident or other issue they normally use specific shops. They have ones that they recommend. You can always call your insurance company and ask who they recommend even if you are not asking to file a claim.
Most places that do paint and body are very proud of their work. They usually will have before and after picture books, walls, boards, or at least access to pictures if not access to people whose cars they have done. If they do not it is a good sign that there is an issue.
The regular auto body shop should allow all of these things. You should be able to check the shop for cleanliness, check insurance companies, and they should show you work that they have previously completed. Usually if they do not allow these things you should check further into the business and make sure that they are reputable. You can always call around and ask if they have a good reputation in your area.