The ones at the park are first come, first serve. No reservations or guarantees of availability. You can rent an ECV from a private vendor, though. I did that when my mother joined us for a trip, and it was great.
I would recommend renting from an outside company, such as Scooterbug. I rented from them after I had my ACL repaired, and it was great. They leave your scooter at the bell hop station at your resort and you can drop it off in the same location. No need to meet them at a certain time (some companies require this). It's much cheaper than renting in the parks and you have the scooter for the duration of your trip, not just while in the parks.
They need to know how much the user weighs to offer you the best ECV. Some of the smaller lighter models won't last well in the park with a heavy person using it.
There is a list of vendors -- both featured and non-featured -- near the end of post #2 of the disABILITIES FAQs sticky. Featured vendors can leave the ECV with Bell Services at a WDW resort. Non-featured vendors will meet you in person. Neither is necessarily better, just whatever you prefer.
Depending on the time of year and expected crowds, you may want to make your reservation a few months in advance. If you wait until last minute they may not have one available.