On startup the oil and most of the other warning/caution lights illuminate briefly. If you pause while on the ON position of the ignition before rotating to start, most of them will turn off, however the oil light (red) and battery (light) will stay red until the engine is started and running, at that point they should turn off.
If the oil light stays on after the car is running, is flashing with the car is running I would turn it off and have a mechanic look at it, it could just be a bad sensor or there could be an issue with the oil system. As always check the oil first before you start up the car while its in a cold state and add if necessary but never overfill.