You can't make reservations directly with the hotel. You either have to call 407-WDISNEY, or the website.
For the best rates, you'll definitely want to call the 407-WDISNEY number. If any discounts come out for the time period you're staying, if you've booked online you can't change your reservation to get the cheaper rate.
A friend of mine (who is not a disneyfile) always calls the resorts themselves and insists that she makes her ressies there. I told her they switch her to the reservation =cro office # and she doesn't even know it, but she refuses, to agree with me.
I found out about the Dolphin teacher rate online and then called the resort to ask a question about it. I did book directly with the Dolphin, but it's not a Disney resort (although very much on-site and very deluxe).
I know you can get a better rate at Swan/Dolphin at times through Hotwire. You also can get some good deals on villas by renting points.