Inspect the turntable base wheels and guides. If they are gummed up with food or other gunk, they will not turn and the turntable will not rotate. Clean as needed.
Remove the microwave case by unscrewing the casing screws with your screwdriver. Locate the turntable motor which will be directly beneath the oven floor.
Inspect the belt that connects the motor to the rotating table. If the belt is broken, replace it.
Touch the probes of a continuity tester to the electrical contacts on the motor. If the tester lights up, the motor windings are good, which means the motor is functional. If there is no light, the motor needs to be replaced.
Check the wires leading from the cord to the motor itself. Look for any breaks in the wire, or a wire that has been pulled off of any electrical connection. Any connection that has been compromised can be soldered back into place, but if the cord is damaged at all, it needs to be replaced.
Attempt to spin the motor by hand if the continuity is good and the belt is in place. It should spin freely, but if it is difficult or doesn't move at all, you will need to lubricate the bearing. Either apply spray or bearing lube to the motor axles to solve this problem, and allow the motor to spin freely once again.