If you ran out of oil you probably need to bleed the air out of the line.
Theres a bleeder screw on the pump, looks like a screw plug with a hose nipple on top. Loosen this a little the hit the reset so the pump turns on. The air and foamy oil will squirt out, so hold a can up to it. Tighten the screw and the burner should fire.
Most delivery truck drivers will do this for you if they know you ran out. If you are at all unsure of your ability to do this, call the oil company to do it.
And if you dont know how old the oil filter is, its probably high time you had a service tech check it out.