There's been at least one thread recommending the purchase of a used bike when on a limited budget. There are a lot of good values out there. However, if you don't know much about bikes or how to repair and maintain them, buying used is a more risky proposition.
Here's a few tips and I hope others will add more:
1. Don't buy a bike without riding it unless you really know what you're doing
2. Bring a pump to pump up the tires if necessary
3. Bring a magnet so you can figure out which parts are steel and which are alloy
4. Don't buy a bike with steel rims and rim brakes. You will not stop if they get wet.
5. A bike that fits is probably the most important consideration
6. Spin the wheels by hand. They should spin smooth and not wobble
7. Make sure the pedals spin smoothly
8. Check for bent or loose spokes
9. Shift through all the gears
10. A road bike with stem shifters will often be of lower quality
11. A road bike without quick releases will often be of lower quality
12. An older road bike will likely be made of steel. There is
often a sticker on one of the tubes indicating the type of tubing.
Reynolds, butted, chromoly are words to look for
that indicate higher quality. There are others. "Hi-Ten" is not
13. Rear Dropouts are the things that the rear wheel is attached to. They can
often be an indicator of quality. If they look like they were stamped out of a
flat piece of steel then it's probably a lower quality bike than one that has dropouts
which have varying degrees of thickness (stamped vs forged).
14. Squeeze the brake handles while not riding. They should pull and retract smoothly.
15. Bring allen keys and an adjustable wrench. Try to adjust the seat up and down. If it
won't move, it may never move.
A lot of the above is what I look for in road bikes, but I'm sure most applies to
bikes of different styles.