First off.....If your car is billowing smoke and sounds like a hammer hitting a tin roof, the repair is probably going to be a bit out of your ability range...proceed with extreme caution.
Otherwise I recommend at least considering tackling the repair yourself. I am not a certified auto mechanic......I've had no formal training in auto repair. What I do have is a father who spent many of my childhood weekends under the hood of one of his old Chevys, cursing occasionally as I passed him various wrenches. It was during these weekends that I, unwittingly, learned a skill that I use quite frequently today.
One thing my father didn't have back then was the Internet. You can find good, helpful information about almost any car ailment imaginable on the Internet. Through discussion forums and chat rooms I've learned the causes of over a dozen different problems in my daily driver as well as how to fix those problems. The money I've saved between diagnosis and actual repair work is with out a doubt into the thousands of dollars.
When attempting your own repair work there are 3 things you must have: A repair manual for the vehicle, a decent set of at least basic tools, and a great deal of patience. Working in an engine compartment will be dirty, and can be painful, with many hot and sharp parts to be avoided. Having bandaids on standby is a good idea as well.
If you can handle some grease under your fingernails, and can follow directions well, many of the common auto repair jobs you will be able to take care of on your own. From changing an alternator to installing new brake pads, the formerly unthinkable will become the now fully possible.
Car work is certainly not for everyone, and to be honest, if my pockets were deep enough, I'm not sure I'd be doing a lot of the work myself. But, there is always a great feeling of accomplishment when I'm tightening the last bolt up, while my stepson is putting the wrenches back in the tool box until the next weekend car project comes up.