Don't buy new
This advice has never been truer. The problem with new cars is that they are just too expensive for what you get. Instead, let someone else buy or lease it brand new, then sell it back 2-3 years later. At this point, the car's price has dropped by as much as 30%. Some people don't like to buy off-lease vehicles, claiming that they are driven harder and maintained more poorly. However, generally off-lease cars will still be covered under the manufacturer's warranty, and you should only buy cars that have a proven track record of being reliable anyways. In other words, a three year old Honda Civic is probably not far removed from a brand new one. Some manufacturers even offer free extra years of warranty for off lease vehicles; this type of warranty is typically not available for brand new vehicles.
Don't buy the extended warranty or gap insurance
These things are a great way for the dealer to make extra cash, but provide little value to you. The dealer will typically try to scare you into buying it, but stay strong. Most people really do not need this coverage, so you shouldn't either.
Negotiate
While the latest trend with car dealerships is to have a no-negotiation policy, everything is in fact negotiable. Remember, that the worst thing they can say is "we can't do that". There is zero harm in asking the questions. If they are firm on the price, ask them to throw in extras: new tires, floor mats, free oil changes, etc. Don't walk away from a good deal just because they say "no" to some of your requests, but don't give into the idea that the sticker price is the final price.
Call around
For better or for worse, car sale contract details are private between the buyer and the seller. This means that you have no way of knowing how much the cars are actually sold for. Your only weapon is getting the dealers to compete for your business. Basically, call 5-10 dealerships within a 100 mile radius of where you live and try to get the best price for the car you are looking for. Remember that since you are shopping for a used/pre-owned car they are all slightly different (this one has a sunroof, while that one has a navigation system, etc.) However, you should be able to get a pretty good ballpark of the price by doing this. After that, go to the dealership where the actual car you want is available and negotiate in person. If they offer you a price that's much higher than the other dealerships, make sure to show them printed out listings and prices you got elsewhere. If they do not bring the price down, simply leave, telling them to call you if the price comes down.
Remember that there are always more cars like the one you want getting to the dealers' lots every day, and the prices for them will keep coming down. Don't be afraid to walk away and have the car get sold: another one will take its place very quickly.