Every guide I can find on the internet tells me to heat it up till the oil is smoking in the pan, but none tells me exactly how long. What is the criteria for knowing that the amount of polymerization is sufficient?
The best way to season cast iron or steel pans is simply to use them. The more you use them, the better they get. Just don't use acidic ingredients, or clean with soap and water. Scrape them out when necessary and wipe out. Once clean, apply a light layer of oil with a cloth. That's it. If heavier cleaning is necessary, put a layer of coarse salt in the pan. Heat and scrape with a wood spatula. Wipe out, and proceed with light layer of oil. Most people over complicate this. You may deal with a less than perfect pan the first couple of times, but this will soon pass as long as you care for your pan as I've described.
This may be a frustrating answer, but the best one I can give after learning it the hard way: you heat it until it is done. And recognizing when it is done is something you have to train in yourself, it cannot be described in words only. In fact, after having seasoned (and reseasoned) several pans, I still don't always catch it at the right time.
Smoke is not a good indicator. Your pan will smoke during seasoning. If you stop the heat the minute you see the first smoke, you won't have a good seasoning - in most cases, you won't have any polymer at all, just liquid oil. At the same time, don't discount the information from the smoke - smoke from burning seasoning looks and smells differently from the smoke from curing seasoning. But this is again something that needs to be practiced.
In practice, if you are not well-trained to recognize the proper state from looking at the hot pan, you have to make a guess, take the pan away from the heat source, let it cool down, and then use your fingers.
- If your pan just has a layer (or a puddle) of liquid oil on the metal, then you used too thick an oil layer, or too low a temperature, or too short a heating time, or any combination of the three. Wipe and restart the process.
- If you have a polymer layer, but it is too light in color and tacky to the touch, you are closer, but still not there. Reheat, without removing the layer or adding new oil, and give it enough time to cure.
- If you have a deep black or anthracite layer that flakes off, you overdid the heat. Strip bare and redo.
After you have done it a few times while watching the pan attentively, you will learn to roughly see the gradual transition while the pan is still on the heat.
Remember that a first seasoning is frequently not perfect. Only use your pan for seasoning-buildup-friendly applications for the first few times, and actively avoid foods that will prevent a good seasoning to grow, especially those containing sugars (attention bacon!) or acid. Crepes are a perfect choice.
For pans without attached wood or plastic parts, it is advisable to season them in the oven, as it is much easier. You can simply keep them there for 3-4 hours, without fear of burning.
Seasoning cast iron is best achieved in an oven, at least when new or for the first few times, using a fat with a high smoke point. Another factor to consider is the quality and interior finish of the pan, as some are junk and/or are poorly or coarsely finished. Method: heat oven to 400 degrees F; place clean, unoiled pan in oven to heat for 45 minutes or so; take pan out and lightly coat all surfaces with fat (I think Crisco or peanut oil is best for this purpose); return pan to oven and let bake for another 45 minutes; turn oven off and let pan cool in the oven overnight. This method works for cast iron as well as steel fry pans of the French type. As always, use and proper care ensure ongoing seasoning, but it may help to oven season from time to time to build up a smooth carbon layer.