When you season a skillet, what you’re doing is cooking layers of oil onto the metal. I’ve asked metallurgists what makes a skillet seasoned, and the only reasonable response I got was from a professor in Missouri who says that heating makes molecules expand, allowing oil and iron molecules to bond (a more precise term would be polymerize). The key is a clan, even, high heat, so don’t listen to those macho types who claim that the best way to season a skillet is on a flaming grill; that will guarantee a black coating, but the oil doesn’t bond to the iron properly and you’ll end up with black flecks of carbon on or in whatever you cook.
To season a new skillet properly, scrub it with soap and water, dry well, rub with salt and brush with vegetable oil or lard. Do NOT use olive oil. Pop it into a medium oven, like 350, and brush lightly with more oil every now and then, say every quarter/half hour or so. Do not let the oil pool up on any surface or you’ll end up with a mini tar pit. Eventually the oil will cook to the metal. The longer you heat it, the better; the skillet might have a brownish/purplish cast, at first, but with use and proper care it will blacken. Wipe the skillet clean of excess oil, and dry it well with paper towels or do like your Granny did and use a wadded-up brown paper bag, either way using salt to scrub away the stickiness, since the surface of a newly-seasoned skillet can be tacky at first. Rubbing it down with salt helps, but you might want to store it in a paper sack for a while.
Don’t use the skillet for anything but baking or frying and wash it with soap and water as little as possible, because doing so too often will damage the polymerized coating. If you find you need to scrub it, use a non-metallic pad with salt, but after you do wipe it down and rub it with oil. If you’ve really screwed up, you’ll have to use a metal scrub and water (or worse, God help you), in which case re-seasoning is in order.