Buying used furniture is a combination of a crapshoot and a treasure hunt. Depending on the intended use of the furniture, various aspects of the process tend to wax and wane in importance. However, learning to gauge value and reliability are going to help you get the most out of your purchase.
The first thing to examine about a particular piece of furniture is material. The more solid wood there is in a piece of furniture, the more valuable it is. Cheap furniture, such as Wal-Mart "some assembly required" furniture is made from particle board with a crappy veneer finish. Particle board is basically compressed sawdust and furniture made from it is practically worthless, especially used. A veneer finish is a thin piece of wood or plastic glued to the top of another material. It's usually pre-stained and is really hard to work with. Don't buy it.
The next material above particle board is some sort of laminated wood. This is usually thin sheets of pressed wood, once again with a veneer finish on top. While this furniture can be pretty and serviceable, it's not going to increase in value and is hard to repair or refurbish without lots of tools, skill, time, and effort. If you see a piece that happens to strike your fancy, pay close attention to the veneer. Make sure it isn't coming loose on any edges and that there aren't any bubbles where the top layer is lifting off of the wood below. Also look for stains and scratches in the veneer, as refinishing veneer is basically impossible for the layman.
The best and most valuable furniture to own is solid wood, preferably some nice hardwood like oak or walnut. This is the furniture that will last forever and increase in value as it ages. For solid wood furniture, the most important thing to examine is the quality of the wood itself. Make sure that the wood hasn't warped, swollen, been eaten by bugs, or otherwise disfigured. Damages to the finish aren't as important, as refinishing solid wood furniture is a straightforward process. It will take some time and effort, but not a lot of skill or tools. However, removing the existing finish can decrease the value of a piece of furniture. Read RainDropUp's excellent writeup on the subject of antique furniture for more information about what to do with your furniture once you've purchased it.
After material, secondary considerations for your purchase should include condition, workmanship, size, and, of course, price. However, each of these should be outweighed by the material of construction for the piece in question. Furniture made from solid wood, even with a poor finish and a shaky leg is worth more than a similar item made of particle board.
When examining the condition of furniture, keep in mind that which can be easily repaired and that which will take some effort. For most pieces, this will depend upon the method of construction used. For example, it is much easier to repair a drawer that uses butt joints than one built using dovetail joints. Also examine the type of damage a piece has taken. A solid piece such as a chair arm that has been broken will be much harder to repair successfully than a loose joint or poor upholstery. Examine the piece closely for signs of previous repairs, such as hairline glue seams, hidden screwheads, etc. Determine how many layers of finish have been applied to the piece if possible, and how much removal work will be necessary (if any). Remember, a structurally sound piece of furniture painted tangerine orange can always be refinished, but that beautiful oak stain won't keep the legs on a chair.
After the condition has been established of a piece of furniture, pay close attention to the workmanship inherent in the construction of the piece. Detail items like carvings and trim raise the value of a piece, as do only wood construction or rare or exotic joints. Also pay attention to the use of different woods or inlays in a piece, such as in the faces of drawers in a dresser. These are the little touches that can add significant value to a piece of furniture. If a manufacturer's mark can be found, a little research on the web might provide some useful information as to the quality or value of a piece.
If you're collecting furniture, or seeking to maximize resale value, then size should also play a part in your decision. Generally speaking, smaller is better as far as furniture value goes. Smaller furniture can fit in more places, requires less effort to maintain or refurbish, can be moved more easily without damage, and is an all around better investment. However, don't let that discourage your purchase of that huge 4 poster canopy bed for the master bedroom. If that's what you want, then go for it. Just remember to take into account the logistics of moving your purchase and take care when moving it to prevent damage.
Finally, consider the price being charged for the piece. Sometimes you can get a deal on a solid wood piece of furniture because it has been painted over or is in poor shape. However, you'll have to spend even more money on it to make it a valuable piece, and plenty of effort on removing the paint, restoring the finish, and repairing any problems with it. Be certain you know what you're getting into before you shell out your hard earned cash.
Used furniture can be found in many different places; flea markets, antique stores, pawn shops, thrift stores, and, of course, used furniture stores. All of these places will have varying amounts and qualities of used furniture and charge various prices for similar items. Keep bargain hunting and eventually, you too, will find that diamond in the rough to bring home.