mousesavers.com is the definitive site focused on saving money at WDW.
But unlike some vacation destinations, you won't find any fantastic deals by going through other sources, travel agencies, etc. If you see what looks like an amazing deal, chances are that it's either not as amazing as you thought or it's an official deal that you can get directly from Disney.
Mousesavers (as well as the discount section here at wdwinfo.com), will give you the rundown of all the latest deals, but here's a summary of the usual discounts.
AAA: this is kind of the standard discount that is almost always available. By joining AAA, you can usually save between 10% and 20% off your room, depending on what level of resort you stay at and what season it is. If you are booking the room only, you can book directly with WDW and ask for a AAA discount. If you are booking a package, you need to book through AAA and only the room portion of the package will be discounted.
WDW discount codes: These are official special deals offered by WDW. People here refer to them as codes because there is normally a 3 letter offer code associated with them. These come in several varieties. There are some offers only available to annual passholders, some available only to florida residents, and some are available to anyone. These also may be deals on room reservations or package deals.
Unless you are taking advantage of a discount that only applies to packages (like the September free dining deal), you can normally save a little bit of money by booking a room-only reservation and buying your park tickets from one of the authorized resellers, like
undercovertourist.com.