Take time to get used to the scooter. Even if you are used to one at home, often the throttles are a little off. If you aren't used to one, remember there are no breaks. Give yourself space on curbs. Go slower than you think. Keep in mind that people will step out in front of you because they may not really see you. It will take more time to get through parks and rides with one so add more time than usual.
I would recommend one of the "Disney Approved" scooter rental companies just because it is a lot easier on you. They deliver your scooter to and pick it up from your resort, you just pick up and return it to the bell desk, they have park access so if the scooter breaks down in the park they can come to you instead of you trying to get a broken scooter out to them. The Disney approved are Apple, Buena Vista, Best Price and Scooterbug.