We are trying to use a potentiometer, and we are trying to find the voltage for programming purposes.

We are using a Bourns 6639s-464-103 potentiometer and when I looked on the specs page it said that it had a VAC of 750.

I understand that this is an AC voltage and that it goes through an AC to DC converter, but I don’t know what the DC voltage will end up being. Will it end up just being the voltage of the analog pins on the roboRIO?

It just takes the voltage from the analog power pin.

The 750 VAC is just the minimum it can withstand before burning out if a surge occurs. It’s not the operating voltage.

On the roboRIO specs, it says the nominal range is 0V to +5V for the analog inputs, so does that mean it will just give the potentiometer a max of 5V?

Yes, nominally.
The actual voltage might be more like ~4.8, so test your pot for the actual min/max signal voltage return.

In code there is an API that returns the actual voltage on the 5v rail that might be useful if you want to know what the maximum signal return might be.