Switch off the power to that room from your main circuit box. Disassemble and remove the existing light fixture, and leave the existing wires hanging out of the wall.
Screw a wire nut onto the end of the green, grounding wire if you have a three-wire light fixture and need to attach it to a two-wire box. Finish the modification by compressing the green wire and nut into the fixture as much as possible to keep it out of the way. If you have a three-wire box and a two-wire fixture, skip to Step 3.
Inspect the wiring box and the light fixture for a screw that appears to have no purpose. This is probably a grounding screw. If your fixture has instructions, you can confirm this by looking for a reference to a grounding screw.
Test the wire box to confirm that it is grounded before using its grounding screw. Wrap the live wire around one probe on a grounding tester, turn the power back on, and touch the screw with the other probe. If the tester lights up, that screw is grounded. Turn the power back off.
Twist the exposed wire around the grounding screw, once the purpose of that screw is confirmed. Tighten the screw down with a screwdriver to fasten the ground wire. If you cannot confirm the existence of a ground screw, screw a wire nut onto the end of the ground wire and compress it into the back of the wiring box to keep it out of the way.