This process takes several steps, so bookmark this page so you don't get lost. You will want to come back here several times for more information.
The first thing you need to do is find the best rate for the travel you have in mind. Use the Travelocity Fare Finder below to start. They usually have the best published rates.
Once you know where you are going, and when, and how much you are willing to pay, visit Priceline to save some serious money. You can make an offer and they will try to find an airline that will sell you their unused seats for quite a bit less than the going rate. I understand 20% off is not an unreasonable offer, and if you offer less you might just get it. If they accept your offer, you are done with this page, but if they don't, you can still come back here and buy the best available seat.