The first thing to do is to check the belt by seeing if it will stay on the platter's inside rim. If your turntable has a plastic platter, you will usually have to remove the "C" clip that holds it onto the turntable. Put the belt onto the inside rim. If the belt does not stay on it when you hold it up in normal playing position, the belt is overly stretched and needs replacement.

If your turntable's belt goes around the platter's outside circumference, check to see if the belt will rotate the motor pulley when you rotate the platter.  This normally indicates sufficient belt grab and tension.

Here are some other things that you can try:

1. Grab the motor pulley and juggle it up and down for a few seconds to make sure it is not binding in any silly way and is free to spin.

2. Then make sure that the belt is looped around the pulley in the middle, between its two flanges.

3. If you hear squeaking coming from the motor, this may help: Remove the platter and check if you can see where the shaft of the motor (would be visible just under the brass pulley) goes into the motor. You can pull the pulley up and down, and see the shaft go in and out possible about 1/16 inch. It does not move that much. Use a toothpick and dip it into a little motor oil (car, grass-cutter, sewing machine, 3 IN 1 oil). Using that oil wetted toothpick, manipulate a single drop onto that shaft at the point it goes into the motor. Then wiggle the pulley, as before, up and down to spread it into the motor's upper bearing.

If this speed condition and squeaking continues, we can only assume that the motor has gone bad.