Two-speed motors usually use two different field coils to produce two different speeds. They usually share a common wire to limit the number of external connections that must be made. Instead of having to manage four field coil wires, there are only three to manage. The most common speeds are low and high. The low-speed coil is feed by a red wire and the common wire and the high-speed coil is fed by the black wire and the common wire. The switch used to control the two speeds also prevents both coils from being energized at the same time.
Place the AC power supply, two-speed motor and DPDT switch on a work table. The DPDT switch has three terminals; use white wire to connect the common terminal of the power supply to the common white wire of the motor.
Connect the black, hot terminal of the power supply to the center terminal of the DPDT switch using black wire. These types of switches use screw-type terminals.
Locate the low-speed wire or terminal of the motor. Connect a red wire between that terminal and one of the two remaining terminals of the DPDT switch. Connect a black wire to the high-speed terminal or wire of the motor and connect the other end of that wire to the remaining vacant terminal of the DPDT switch.
Turn on the power supply and throw the DPDT switch so that the center terminal connects to the red-wired terminal. The motor should run at low speed. Now throw the switch so that the center terminal connects to the black wire. The motor should now run at high speed.