First thing's first, nothing is going to replace general mechanical knowledge or knowledge of the repair's being done. Take your car to several shops and get some diagnosis and estimates.
Depending on the problem, they may be able to give you a semi firm estimate or (on older car's where chasing problems might occur) they may leave it open.
Research the problem and the solution on the internet. Again if you have a basic knowledge of mechanics this will really help out. Car based forums (much like detailing based forums) have really helped to educate the general public with the generosity of information shared by their members.
Research the shop. Read local reviews on posted on the internet of the shop and/or speak to customers.
Knowledge is key. Now if this is a simple, low cost fix (like changing the spark plugs) it probably isn't worth your time to research too much. But if we are talking out a complex repair with a bill in the $1000s of dollars, spend the time arming yourself with as much information as possible. The two hours of research could saves $1000s off a large bill, which would be the most money you might make per hour all year.