Shut off power to the 14-3 circuit at the main power panel. Use a voltage meter to verify that the power for that circuit is off. A 14-3 circuit carries 220 volts as opposed to a 14-2 circuit, which only carries 120 volts.
Open the electrical box that houses the 14-3 cable. Run the 14-2 cable into the same electrical box as the 14-3 cable. Strip 1/2 inch of insulation off of the ends of the black and white wires in the 14-2 cable.
Look at the 14-3 cable. The 14-3 cable has one black wire, one white wire, one red wire, and a ground wire. The black and red wires are the two hot wires of the 14-3 wire. The white wire is shared between these two hot wires. The fan can be powered by using the red and white wire or the black and white wire.
Identify what other fixtures are powered by this circuit and identify which half of the 14-3 wire each fixture uses. The fan should be connected to the side that has the fewest active fixtures. The idea here is to try and keep the two sides of the 14-3 wire as equally loaded as possible. This helps keep the wire from overloading.
Connect the black wire of the 14-2 cable to the red or black wire of the 14-3 cable. Connect the white wire of the 14-2 cable to the white wire of the 14-3 cable. Connect the ground wires of both cables together. Use plastic twist caps to hold the wires together.
Close the electrical box and turn the power back on. Test the fan.