How to build a steerable remote-controlled vehicle with just 1 motor?
This can be done without a caster wheel as well:

Start out with a three wheeled vehicle, with two wheels in the front and one smaller wheel with less traction than the front wheels in the back. All wheels need to be fixed.

One of the front wheels is attached to the motor. This might need to have some gearing to get an appropriate speed.
The other front wheel is unpowered but can only rotate forward by adding a ratchet:  



The back wheel is unpowered.

Driving forward the vehicle will more or less move straight, guided by the rear wheel.
Driving backwards the ratchet will engage, stopping one wheel. The vehicle will now turn.