Equipment intended to be used in different countries often has a transformer that either has two primaries of 120 volts each or it has a center tapped 240 volt primary.
The first would have 4 wires and the second would have 3 wires.
You should be able to work out which wires are which using a multimeter on the "ohms" scale.
As your supply is 120 volts you may be able to use just one of the input windings if the transformer is the first kind.
If it is the second kind, ie with a center tapped transformer, you would use one of the outer wires and the center tap as the two inputs to your primary.
You would open the box and connect to the terminal block where the transformer leads are anchored. Do not attempt to join a new cable to the wires that come out of the power supply.
Follow the same type of anchoring that was used for the original power cord.
Don't touch anything when the power is connected.