If the motor runs but the blower doesn't move air, the belt that connects the two probably has broken. Replacing it is easy.
First, turn off all power to the unit, and turn off the gas at the gas valve that serves the furnace. Remove the door on the front of the furnace cabinet to give you access to the blower. (It may be on a slide-out drawer, or the blower pulley and motor will be easily accessible.)
Check the number stamped on the belt, and get an exact replacement from a home center or heating supply outlet.
You can usually slip the belt on the motor's (smaller) pulley first, and then start it on the blower pulley. Rotate the blower pulley by hand, holding the belt in place but keeping your fingers from being caught between the belt and pulley.
The belt should slip right into place. If it seems too tight, it may be necessary to adjust the motor mount to provide more slack. Then retighten the tension once the belt is in place.
Check the manufacturer's specifications for proper tension; in most cases, the belt should deflect about an inch when you press down on it.