Whether you're getting your own car fixed, or buying a car that was previously damaged, knowing the extent of the damage and how well it was fixed can determine the value of the vehicle, and whether or not it's in running condition. Some mechanics run backwards shops, in which they make more money by only fixing the external damage so the car appears fixed, even if it isn't. Other, more trustworthy mechanics will charge an arm and a leg to properly fix a damaged vehicle. But unless you know a lot about cars and fix it yourself, there's really no foolproof way to assess how well repairs were implemented. Even so, it's not a bad idea to take some precautionary measures to get at least an idea of what was done to the car
Do it Yourself
For those lucky few of us who happen to be pretty handy with car mechanics, you can fix the damage yourself, if it's not too severe. Sometimes, special tools, machines, and equipment are required for specific repairs. In that case, it's probably necessary to take it in. If the problem can be solved with common garage tools that most self maintenance people have, then go ahead! Make sure you know exactly what the problem is, and what you're doing, lest you damage it further or fix the "wrong" thing. For cosmetic damage such as dents and dings, there are lots of DIY dent puller kits that have a pretty high success rate. Unfortunately, they tend not to work on crease dents. Repainting your own car is also not the best idea, unless you're going to take the time to sand it back down to sheet metal, and add all the necessary coats of paint and varnish.
Be careful when choosing a mechanic to make repairs on your vehicle. Though any random mechanic can probably get the job done, they may not do it too satisfactory conditions. It's best to go with somebody a family or friend recommended, somebody who you've gone to for a while and know you can trust, or, even better, a friend of yours who happens to be a mechanic. These people are more likely to give you good deals, and provide excellent service to your vehicle. Sometimes, mechanics will even let you watch the process (if it doesn't take too long) so you can supervise what's happening to your car and what they are fixing. Though this won't help if you don't know anything about cars, it may scare bad mechanics into doing a decent job.
Assess your vehicle
After getting it back from the mechanic, or after buying a previously damaged car, try your best to do a self assessment. Does it appear to drive well? Does the wheel pull or are the tires not properly aligned? Do any maintenance lights appear on the dash? Check the tire pressure, and look for any dents on the exterior. If everything seems okay, it just might be. Check everything again after driving it again for the next few weeks, as some problems may not manifest themselves until some time has passed. Though knowing exactly how well the damage was repaired is difficult, you can at least get an idea by taking some initiative and viewing things for yourself.