Welcom to the DIS!!!
You have two options for renting on Disney property. You can head to the Car Care Center, which is on the way to MK. You can call them the day before you are to pick up your rental and they will arrange for a shuttle to pick you up and take you to the CCC. Then, you reverse it when you return the car.
Other option is renting at the Dolphin. No shuttle there, you would have to get to Dolphin on your own. I rented there in May and it was very easy...arranged for a 3:00 rental, got there at 3, did the paperwork, they handed me the keys. We walked back over to Epcot for the rest of the day. After IllumiNations ended, at 9:30ish, we walked back to the Dolphin, handed the keys to the valet, who then drove the car up to the front door for us. And off to POP we went.
There are also some rental companies in DTD as well, but I'm not sure where or which companies.