How do I rig a corded electric motor to run off a battery?

I think you need to recheck the motor. If by corded, you mean something you plug into the wall then it's AC. If it's 120 volts then it's likely to be 120 Volts AC. DC motors tend to be 12 Volts, 24 Volts, 36 Volts, 48 Volts, or 96 Volts. Besides it would take a lot of batteries to get 120 Volts DC.

Because you are going DC batteries to DC motor the connection to make it run is very simple. 10 - 12 volt batteries in a series will give you 120 volts. Anything less will make the motor run slower than its rated RPM.

Volts x Amps gives you the wattage. The amperage will give you a rough idea of the time you will be able to operate the motor. A battery system rated at 96 amp-hours would allow your 12 amp load to run approximately 9 hours.

What gets a bit more complicated is trying to control the speed of the motor. For this you will need a device to adjust the voltage rated for the load you are using. A DC speed controller can be as simple as a rheostat.

If you really want to use that motor...

Mount a couple of deep cycle batteries in a bike trailer and get a 2000 Watt inverter.

This will let you run the motor on AC. This is not an ideal setup but it could be a fun prototype.

For about the same cost (or cheaper) you can get an electric bike conversion kit. All the engineering is done for you. Just replace your hubs/wheels and off you go.

Sure you could do that. But don't suppose that you'll get perpetual motion. Each and every factor of this cycle will suffer an energy loss. The batteries will lose cost rather swiftly. Certainly the cycle will run less time than for those who took the alternator out of the circuit, just strolling the motor at the same velocity, from the batteries but turning nothing.