UPDATE : The August 1989 draft script for BTTF II+III contains some additional info in the letter that the Doc (in 1888) sent to his future self in 1953
"Upon landing, I bottomed out the car, destroying the drive train and
flying circuits, making it impossible to get the car up to 88 under
its own power"
It seems that the car came in at a shallow angle and landed flat against the underside of the car before sliding along for some distance.
After studying the original footage for the DeLorean flying sequences, it's clear that the car actually has three main flight systems, not just one;
When the doc states that the lightning "blew out the flight circuits", its pretty likely that the anti-gravity was damaged (we don't see the DeLorean flying again) but that could have left the wheel thrusters relatively intact.
Assuming the flight systems were designed to 'fail safe' in the event of a catastrophic loss of power, these thrusters could then be used to pilot the car to a soft landing. Certainly when we see the DeLorean next (in the mine) it appears to be intact and undented.
As to how the Doc rotated the tyres back into their non-flight configuration, I think we can reasonably assume that that was simply a matter of jacking up the car and physically moving them.