Step 1: Wash and Dry Your Pan
It's hard to say exactly what happened to that skillet between the time it came off the factory line and when it arrived in your kitchen, so you'll want to wash it before starting to season. Give the pan a good scrub with warm, soapy water, then dry it thoroughly. Even after towel-drying, some surface moisture may remain, so your best bet is to put the pan on a stovetop flame for a minute or two to drive off any lingering water.
Step 2: Rub It All Over With Oil and Buff Well
Now that your pan is clean and dry, rub it all over, inside and out—including the handle—with cooking oil. Here at Serious Eats, we're fans of unsaturated cooking fats, like vegetable, canola, and corn oil, for seasoning our pans. Not only do we always have them on hand, but they work well and are easier to spread than saturated fats, like shortening or lard. There's no need to go out and buy any special oils just for seasoning!
The key here is to rub the oil all over, but then buff it so thoroughly that the pan no longer looks even the slightest bit greasy. Even a small amount of excess oil on the pan can pool during seasoning, forming little hardened droplets on your cooking surface, or turn sticky if left unused for a few days.
Step 3: Heat It in the Oven
Put the oiled pan in a preheated 450°F oven, and leave it there for 30 minutes. It may get a little smoky, so keep your kitchen well ventilated. It's during this time that the oil will polymerize and form the first of several hard, plastic-like coatings you'll be laying down.
While it's not essential, especially if you've buffed away all the excess oil, I like to turn the pan upside down and put a baking sheet or piece of foil underneath. It's just added insurance against any excess oil that decides to run and pool, since gravity will pull it out of the pan.
Step 4: Repeat 3 to 4 Times
When the half hour is up, take the pan out. (Remember: It's hot!) Now rub it once more all over with the oil, buffing it out as before. Then put it back in the oven for another 30-minute spell. All in all, you'll want to do this oiling-and-heating process three to four times, to set down a good initial layer of your own seasoning.
Once you're done, just let the pan cool down. It's now ready for cooking.