After purchasing a used car, first check to see if there is an existing warranty on it. If the terms and coverage of the warranty are not to your liking, check to see if the warranty can be canceled. Some warranties are transferable but can only be canceled by the original purchaser. Shop around for a warranty that covers everything you think you will need.
A used car warranty, as a type of extended warranty, may be expensive. However, if you plan on putting this car to considerable use, a used car warranty is probably a wise decision. Similar to insurance, you do not usually want the cheapest warranty on the market. If you have price checked with a number of different companies and one company is selling warranties for an unbelievably low amount, then there is probably a reason. A quality warranty with a solid company that will cover the costs at claim time should be your priority.
This is not to say that the price of the warranty should not play a factor. If the cost of repairing the "normal" mechanical failures of the car will not exceed the amount you pay for the warranty plus the deductible, then you may want to reconsider. Often times though, you purchase a warranty precisely because you do not know if a pricey component in your car will break down.
You can get a better idea of what type of coverage you will need by taking the used car in for an inspection by a certified mechanic. An inspection is not a psychic reading, so do not expect a mechanic to be able to magically tell you what will break and when. Rather, they can give you a rough idea of what is still in good condition and what is not.
Once you are down to the actual buying of the warranty, be sure you triple read everything before you sign the dotted line. Check the Better Business Bureau and Standard & Poor's for ratings, comments and reviews to find a credible company.
Contract terminology varies from company to company. Two companies may try to sell you used car warranties with similar price tags; both contracts may contain the term "comprehensive", but they could very well mean different things. Have the dealer explicitly spell out what all the ambiguous terms mean in writing.
Another important factor when comparing used car warranties is the amount of flexibility they grant you to choose your own mechanic. Preferably, the warranty should also pay for your claims up front and directly to your repair facility or dealer