I'm assuming the oil level is okay and the motor doesn't sound starved for oil, i.e., the oil pump is okay. The oil pressure light on the instrument cluster is usually wired to the oil pressure sender (near the oil filter). It's a simple pressure switch that goes electrical-open (12V circuit) when enough pressure is applied. So, when you turn your ignition on, the switch starts out closed, the 12V supply is shunted to the ground, and you have your oil warning light ON test. Then, as soon as the oil pressure exceeds the threshold, the switch goes electrical-open which causes the oil pressure light on the instrument cluster to go out. Since your oil pressure light stays on, it's either:
1. The circuit is shorted to the ground, either at the switch or wiring.
2. The oil pressure sender is defective.
3. The oil pressure is truely low.
The last can be verified by a mechanical gauge plugged in place of the oil pressure sender.