Parts of the Kiln: This is a Gare 1818 with a 6.5" collar. It was built in the 1980's and is equipped with a Model K kiln sitter.
Buying a Used Kiln:
Most kilns have the same basic parts, so the kiln picture above should be useful for most kilns. The biggest difference in kilns (at least for beginners) is the type of controls and energy source. Some electric kilns have digital controllers with no switches, while some have knobs instead of switches. Collars are optional, some collars have their own elements while some don't.
My kiln is a twenty year old Gare kiln, a terrific find from Ebay (search ebay for electric kilns). Used kilns are a great way to save money, but you need to know a little about a kiln before purchasing it. Ask the seller where it has been stored, when it was last fired, how well it fired, whether all of the elements are working, and how well the kiln sitter works (did it overfire/underfire, etc.). If a kiln has been stored outside, you should probably pass; water is not a kiln's best friend.
If you have enough basic knowledge about kilns and electricity, you can fix almost any problem that you'll find in an electric kiln. You can adjust a kilnsitter if it is overfiring/underfiring. Broken elements can be replaced (this is where some electrical knowledge comes in handy). Kilnsitters, tubes, sensing rods, and cone supports can all be replaced. Even fire bricks can be repaired or replaced. The biggest issue is cracks, either in the bottom of the kiln, or worse, in the lid. Small cracks on the bottom of the kiln can be covered by a kiln shelf or sealed with kiln cement.
A little internet surfing can go a long way in helping you to figure out if a used kiln is worth purchasing. While most things can be fixed, at some point the cost of the repairs far outweighs the savings you'll get from a used kiln. Check out Euclid Kilns to find reasonably priced replacement parts for older kilns. Want to skip the hassle of a used kiln? Check out Buying a New Kiln for benefits of buying a new kiln and to read about my experiences with a used kiln.