How do I find the replacement number? I have called a lot of places but no one seems to know. I have 3 small children at home and I live in North Texas. It gets really hot in the house especially with no wind blowing in the windows from outside. I need to buy the motor ASAP.

Condenser fan motors are fairly generic. You don't need an A.O. Smith fan motor, you just need a fan motor.

There is a nomenclature tag on the motor. It will tell you what you need to know, voltage, amperage, horse power, RPM and direction of rotation. Look at the number of wires and mounting.
Alternative is to take old motor to heating and A/C supplier and ask for replacement. Also get a new capacitor for the new motor, so take your old capacitor also.

These motors are pretty reliable. Tell us why you need to replace.