How to clean a cast iron pan

1. Clean off any food residue. One good way to do this is to fill the pan with a little bit of warm water and to scrub it with a chain mail pad. You can also use soap if you want, but generally you don't really want to get rid of any grease left over from cooking (it'll become part of the seasoning).

2. Heat the pan on medium low for ≈5 min to dry it off completely.

3. Rub the pan with just enough oil to give the whole thing a light coating.
   Then heat the pan on high until the oil is lightly smoking and the pan is thoroughly heated, probably 1-2 min. Remove from heat and let cool before putting away.

   The best oil to use for seasoning cast iron is flaxseed oil. It's the only edible "drying" oil, but it's expensive and hard to handle (e.g. it needs to be refrigerated and kept in the dark, and it can combust spontaneously).
   Canola oil seems to work too, so it's an easy alternative.

References

http://www.seriouseats.com/2016/09/how-to-clean-maintain-cast-iron-pan-skillet-cookware.html

Suggested heating the oiled pan until smoking, which made a lot of sense to 
me.

http://sherylcanter.com/wordpress/2010/01/a-science-based-technique-for-seasoning-cast-iron/

Why drying oils like flaxseed oil are the best for seasoning cast iron 
pans.