Questions to ask:
1. Where was the vehicle serviced? do you have maintenance records?
2. Has this vehcile been in an accident? if so, is it a salvage title?
3. Is this an auction vehicle?
4. Does it have a clean title?
5. HOw many owners has this car had?
First off, find a few models that fit what you need- and then look up reliability raitngs and user ratings to see how well the car will suit your needs.
After you have decided on a few models, start checking out craigslist.com, vehix.com, autotrader.com, and dealers/newspapers in your area for the cars you want, then go and look at them/test drive them.
After you lower it down to 2-3 cars, this is where you need to inspect the cars. Does the transmission shift smoothly when you drive (you shouldn't feel the tranny shifting, or hear a whining noise- if you do this is a bad sign!). Do they have maintenance records? Do all 4 tires have the same amount of tread on them (unequal tread can be a result of suspension problems).
And after you have narrowed it down to a car, have a mechanic check it out (get a CERTIFIED, trusted mechanic- if you get a cheaper mechanic, he could just lie to you to make money). The 50-100 dollars that you spend on the trusty mechanic can save you thousands in repairs. Usually a mechanic can tell you how well the engine was taken care of, how long the car will last you, what maintenance you need, if there was frame damage, etc.
carbuyingtips, like the first guy suggested, is a great place for more advice. Good luck on the job hunt!
and remmeber: If it sounds TOO good to be true, it probably is- those scams are getting really complex and harder to detect day by day