How early do you suggest booking a room and what is the best way to do it (travel site, disney site, calling the resort, AAA (or other) travel agent, etc)?
The best way for me is calling Central Reservations at 407-WDISNEY. That way, I get a live person to talk to. I use the internet for all my other travel arraignments but never for Disney World. I've used a travel agent just once for a Disney cruise and that's only because my mother-in-law, who was paying for it, insisted on it. I don't believe (in fact, I'm 99.999% positive) that the Disney resorts themselves do not make reservations at all.
As for how far in advance you can make a reservation, I've made them 15 months in advance. If there is a resort increase, though, you will have to pay the difference. Through Central Reservations (not the Walt Disney Travel Company), a room only reservation requires a one night fully refundable deposit within the first 14 days of making your reservation. You can cancel up to five days before your arrival with no penalty whatsoever. The Disney Travel Company will require full payment 45 days before arrival date. The phone number above goes to both places.