Single phase motors can be reversed by either swapping the starting winding or the running winding around but never both. When both windings are swapped around, the motor still runs in the same direction as it did before.
To determine which winding is which, a multimeter must be used to measure the resistance of each winding. The winding with the higher resistance reading is the starting winding while the winding with the lower resistance reading is the running winding. To determine the resistance of each winding, set the multimeter to read in ohms.
Once the starting winding has been determined, use the motor's wiring diagram to determine which starting winding leads to swap. If the motor does not have a wiring diagram, begin with the starting winding lead that is connected to the capacitor or centrifugal switch. Take the end of the lead that is not attached to the capacitor and attach it to where the second starting winding lead meets with the two running winding leads. Then, take the end of the second starting winding lead that is attached to where it meets with the two running winding leads and attach it to where the first starting winding lead was originally attached to.