If a vehicle starts fishtailing from side to side, you need to countersteer earlier and faster. Using a steering wheel (or gamepad) is highly recommended.
Cars with more weight on the rear wheels can have a tendency to initially understeer with throttle application, and then oversteer suddenly. This is called "snap" oversteer.
Overheating coolant may vaporize, making a hot engine harder to cool down after long periods of overheating. You can recover the vehicle using [action=recover_vehicle] to reset the coolant level.