I am a grandmother and an old fashioned Southern cook from a long line of Southern ladies. All our family has ever used is cast iron. I have a couple of pieces that have been handed down in the family that are over a hundred years old that I use almost daily. I have a skillet I save for cornbread that I do not use for frying so as to preserve a good smooth surface and my bread comes out without sticking. I bake homemade biscuits in my pans which is also good for making a nice smooth surface. I use only cast iron skillet, no others and have for the past 40+ years that I have been a homemaker. I think they are the best of the best and will be giving my legacy family pieces to my granddaughter next spring when she gets married.
Depending on the amount of cleaning you need to do to cast iron the methods are:
Light soil for everyday cooking: Use soap and water with a greenie pad or other pad, just as you would any other soiled pan. Even a choreboy metal scrubber won't hurt cast iron. Don't leave soaking in water as it could cause a pan to rust. Mild soap that is rinsed off right away will not soak in nor affect the taste of food cooked later. You can also put the skillet/pan/pot on the stove and boil water in it to remove food from the inside. This tends to remove the “seasoning” from the interior and so the pan is not so non-stick as a well seasoned pan. The outside will still need to be cleaned and that requires washing in the sink. Dry the pan as soon as you wash it. NEVER EVER EVER put one in the dishwasher!
Moderate soil from baking in a pan: Put water in the pan and soak for about thirty minutes to an hour and scrub as above. This amount of soaking with a well seasoned pan will not hurt it at all. This is how I clean my dutch oven after baking chicken or a roast. Scrape with a metal spatula if you need to get chunks of material out of the bottom.
Badly soiled or baked on gunk: About every couple years or so my pans get a crusted on coating of grease on the outside that doesn't come off with ordinary cleaning. At that point I gather up which ever ones need it and put them in my self-cleaning oven and let it run through a regular cycle. I have rescued pans from yard sales and thrift stores and restored them to new life this way. I have a huge iron water kettle that I got for $2 at a yard sale and was heavily rusted on the inside, it required two trips through the oven to completely restore.
Seasoning new or deep cleaned pieces: When you get a new piece or have cleaned one in the oven it must be seasoned. Use regular shortening or lard for this process, NOT cooking oil. Oil will leave a sticky residue. Preheat your oven to 300 deg. Put a little grease on a paper towel and rub the grease all over the iron piece, inside and out. Bake in oven for about 30 minutes, there may be some light smoking from the oven but if you did not use much grease it will be minimal. Remove piece from oven and let cool. Repeat this process two more times to get a good seasoning on the pan. Do not use too much grease each time as it can leave a sticky residue on the pan or burn on the grease and you would need to start over and re-clean it. You should not be able to see any clumps of grease, just a shiny surface if you have rubbed it in well. Any time you have little rust it will not harm a piece as it can be wiped off, given a light coat of grease and placed in the oven to season.