Turn off power to the furnace at the service panel. Open the furnace door and locate the squirrel cage blower. The motor is located in the middle of the blower and is accessible from one side. Cut the wires going into the motor, as close to the motor as possible. Do not cut any other wires in the compartment. If you have unimpeded access to the blower, simply unbolt it from the furnace and remove it. If there is an electrical box in the way, unmount it first so you can get the blower out. Keep notes as you work to help you remember how everything should go back together. Clean out the blower compartment and clean or replace the old filter. The filter needs to be cleaned every month. Poorly maintained furnaces and filters are what cause blower motors to burn out.
Remove the ground wire that attaches from the motor to the blower. Remove the bolts from the bracket that mounts the motor inside the blower. Turn the squirrel cage over and loosen the nut as far as necessary to allow the shaft to move. Turn the cage back over and remove the motor. Take the bracket off the motor so you can reuse it with the new motor. Clean the blower.
Replace the old motor with one that has the same horsepower and RPM. Put the old bracket on the new motor and insert the motor in the blower. If the new motor has oil ports, make sure they are facing out and are not blocked by the bracket. Tighten the shaft nut and bolt the bracket to the blower, taking care to keep the motor centered in the blower so it does not interfere with the fan. Attach the ground from the motor to the blower. The new motor will come with a label that explains how the wires must be connected. Connect the wires from the blower to the furnace either before or after the blower is bolted back into the furnace, depending on which is easiest. Check that the fan spins freely. Then close up the furnace and turn the power back on to test it.