How to check electric motor with 3 terminals for bad capacitor or bad winding with multemeter ?

Take an ohm meter and put it on terminal 1 to 2. Then 1 to 3. Then 2 to 3. See if the resistance is the same. If one is infinite ohms then there you have an open circuit. The wiring is bad or fried.

Capacitors are a bit different. It would be best to take them off and to test them individually. However, if this is a the phase motor it most likely won't have capacitors. Capacitors are used in two phase motors.

Anyhow, you take the capacitor and connect a battery to it, positive to one end and negative to the other. Then disconnect it and check its voltage. If it still has a voltage it's good.

If you can't get the capacitor off the motor you'll need an oscilloscope and a variable AC source. If your fuse is being blown then either the motor has a short circuit, or it's not turning either from a bad capacitor or it's stuck, or your fuse is less than the amperage required by the motor.