In the restaurant, we just poured some coarse salt into the pan and put it on high heat (gas range). Then tossed the salt around and poured out the results.
At home, with the electric range top, I put my carbon steel wok on a burner on high (it's scary, but it works) and watch as everything burns off and the carbon steel "steel" look returns.
The brilliance doesn't last but the surface does. I use a cotton rag that is very lightly dabbed in peanut oil to brush the surface while it's hot.
And then it darkens when it's cooling/cooled.
Don't hesitate to go hot, really hot. Just be safe at the same time.
It might be better for you to understand some of the factors involved, and make your own decision how to treat your pan. Below is some basic information I think you will find helpful.
Background: I've successfully reclaimed old, rusty pans, fixed a few that family put in the dishwasher (TERRIBLE IDEA) and so on, and maintain my own regularly.
Cast iron is "seasoned" when it develops a highly carbonized and oxidized surface. This surface coating is both harder and more slippery than the plain iron.
This surface only truly develops with 3 things: High heat, carbon and oxygen in the presence of your pan.
The heat can be provided by a stove, oven, campfire, grill, torch, etc.
The Carbon can be provided most effectively by some kind of oil. I prefer crisco/shortening most. Baconfat second, but that's just an opinion.
The third thing is oxygen. That's in the air, so it is both free and plentiful.
Now, other things to consider. If you have an unseasoned, rusty or poorly seasoned pan, it actually might be best to "start over". Using some kind of abrasive (steel wool, sos pad, even light sand paper) you can remove any unwanted coating, until you get to the grey, dull iron underneath.
Then apply oil, and apply high heat in the presence of oxygen.
Sometimes this coating may take several applications to develop, and will actually get smoother and darker with use. Rubbing with things like salt and whatnot can actually act to kind of polish the surface.
And the best part is, if you truly don't like how an application turned out, scrub it raw, and start over. You'll be removing almost immeasurable amounts of the iron. I have my GREAT GREAT Grandmother's skillet, and it has been seasoned and re-seasoned perhaps a hundred times in its life.
The rest is mostly guesswork, opinion and conjecture.
I hope this helps.
Best Answer
What you're seeing is the bare metal being exposed where the black coating has worn away.
That black coating is the factory's "pre-applied seasoning" - which is universally not a very good seasoning. The pre-applied seasoning is supposed to be a value-add, so a home chef can begin using the pan immediately. In my experience, this coating comes off easily and doesn't have much anti-stick properties - so you'll nearly always re-season the pan anyway. The pre-applied coating mostly serves as an anti-rust coating while sitting on the store shelf, in my opinion.
The lines you're seeing develop are likely from how you "buffed" in the oil during your seasoning - they look like streak and drip marks. The darker areas are thicker seasoning.
I season by pouring in my oil, rubbing it with a paper towel until the entire pan (inside and out) is coated lightly and the oil doesn't drip or run, then put it into the oven for an hour upside down (with a baking sheet on the floor of the oven to catch any drips). After an hour, turn off the oven and let the pan cool inside the oven. Repeat a couple times, then get cooking! If your wok has a wooden handle, you'll need to do it on the stove top instead, but the process is pretty similar.
Over repeated use (cooking, cleaning, re-oiling), the rest of the coating will come off and be replaced by your own developed seasoning. So, start cooking!
Just be careful how you clean it to not destroy your seasoning!