Turn off the furnace and refill it with heating oil.
Bleed air out of the furnace by attaching tubing to the bleeder valve on the furnace, which is normally located on the side of the fuel pump. Run the tubing to a bucket that catches the oil as it comes out.
Turn on the furnace so it starts to pump fuel. Press and hold the reset button for thirty seconds. This should prompt the furnace to restart. Open the bleeder valve by turning the valve screw with a wrench. Close the valve once the oil starts coming out in a steady stream since this means the air is out of the system and won't interfere with the fuel anymore. This also gets rid of sludge that may have gotten in the lines when the fuel first ran out. Shut off the bleeder valve if the furnace turns off and reset it again.
Disconnect the hose from the bleeder valve once the furnace is running properly. It may take several resets before the furnace ignites and resumes running properly. Repeat the steps if necessary to ensure no air remains in the system.