How to replace on old 2 wire single light switch with a 3 wire?
Your original switch sounds like a single pole single throw (on off). Your new switch sounds like a single pole double throw (referred to as a 3 way)
You can make this switch work by connecting 1 of the wires to the black screw. Then the other wire to one of the 2 other screws (notice a 3 way has no on off) turn the power back on and see if up on, if correct turn power back off and push switch back in, if backwards decide which would be better.
Turn switch and stuff it back in or move the 2nd wire (not black screw) to the other terminal. With old wiring I prefer to not twist the wires as the insulation may be brittle so moving the conductor over to the other connector may be best, then push it in and tighten.