I think the swapping will be done at the supercharger stations. Eventually every supercharger station will have 4 charging ports + 1 swap station. If you look at the pic of the 4-port supercharger station with an obelisk, there's one empty space to the right of the first charger. The swapping station will be there.
I envision it as a low height platform between guides for the car wheels. The car drives over this platform. Ideally the station wirelessly communicates with the car, and the car drives the last meter automatically. The station has a laser to determine when the car should stop, and the car stops automatically.
The batteries will be underground. When the car stops, the lid under it will open, and a robotic swapping thing will come up to remove the battery. It will not be a general purpose manipulator (arm). It will be a simple flat platform that goes up, aligns a little with the battery, unscrews/unlocks the battery and pulls it down.
As soon as it goes down and to the side (underground), the second similar platform with a battery goes up and attaches the new battery to the car.
All this can take very little time.
The station can wirelessly exchange info with the car before and during the swap. For example, if the battery in the car is worn-out too much, the station can refuse to swap it before the car even gets close to it.
The battery health can be measured in points. If my battery is 100 points, and I swap it to a battery with 90 points, my balance is 10 points. If the opposite happens, my balance would be -10 points. The points may be converted to money (credit or additional fee for the next battery swap).