Hi there--my Mom and I took her
scooter to WDW from California last November. It was actually very easy--we were flying on Delta, but I think it would be similar on most airlines.
She rode the scooter all through security (of course, she was subject to extra security) and to the gate. At the gate, the agent gave her a special gate tag, and then she rode it all the way to the door of the plane. At that point she used her walker into the plane
(but I believe they have special wheelchairs if you can't walk). The luggage people took her scooter and took it to the luggage hold in the plane.
We of course, loaded first with special needs.
At the end of the flight-we were last off the flight, and the scooter was waiting for her at the door of the plane.
You do need to tell the airline ahead of time what type of batteries your scooter takes--if it's "wet cell" they have to have a special container for them. Most scooters take "dry cell" batteries and they've good to transport without special handling.
Hope that helps!