I have been told that a weak capacitor may be the reason for my furnace motor is heating up and shutting down after only an hour running the A/C. Where do I find this capacitor, what does it look like, and approximately what do they cost.

Most motors have the capacitor mounted on them or connect with wires FROM the motor.
Follow wires from the motor.
Maybe 1 1/4" diameter and about 3" long.
It is an easy and cheap first thing.