I prefer to do my cooking on cast iron cookware. Cast iron is an astonishingly effective non-stick surface. It heats evenly and is super simple to clean. I can think of only two negatives: it is heavy, and maintenance is very different from my other pots and pans.
I have a set of more-common-today stainless/copper cookware. After using a pot or pan, I scrub it out in the sink with hot soapy water, dry and put away. Sometimes, when I'm lazy or just so inclined, I even put it in the dishwasher. It is what most people are used to now.
Because cast iron is seasoned to create its non-stick properties, and to keep it from rusting away, it needs different cleaning and maintenance. The coating of seasoning on your pan is a layer of polymerized oil. It's tough, and keeps air, water and food from ever coming in contact with the highly reactive iron surface. Most of the time cleaning it is super simple: while the pot or pan is hot, throw in a large handful of kosher salt, and using a wadded up paper towel, you scrub the sucker out.
You toss away the salt, wipe out the dusty remains, and let the cookware cool. If you want, and I do every 3 or 4 uses of an item, you can wipe it down lightly with your cooking oil of choice. I recommend wiping it off as much as you can, so the layer is just super thin, and heat the pan until it smokes.
On the rare occasion that stuff gets too cooked, baked or burnt on, and scrubbing it out with salt won't clean it enough, you can fill the pot or pan with water and boil it for a few minutes. Most everything cooked on will come free, or be easy to scrub loose after.
Sometimes I do the scrubbing with a chainmail scrubber, other times with a heavy duty kitchen sponge. The seasoning can take it, just make sure to completely dry the pot or pan, perhaps giving it a light coat of oil and some heat, as above.
Boiling, or just washing out in the sink with hot, soapy water, can temporarily discolor your seasoning. You should feel absolutely free to do either, however. If you are concerned, wipe the object down with cooking oil and re-season it. Simply put the lightly oiled iron in a cold oven, turn the oven to 400ºF and let it bake for an hour after the oven reaches temperature. Turn off the heat and leave the object in the oven until it is cool. The color should be pretty even again. Give it a light coat of oil and wipe off, it'll look fine.
Over time, regardless how hard I work to keep one particular skillet clean, a tacky film forms on the outer sides. If ignored this layer of soon-to-be-rancid-fats gets gross. The layer is formed by oils that heat up on the cast iron, but not hot or for long enough to polymerize. If they did, they'd add to the layers of seasoning. Generally, as you cook, fats on the cooking surface will continue to bond to the seasoning, and undergo the same chemical reaction as the initial seasoning. This stuff isn't making the jump, and salt takes a whole lot of effort to get it completely off. There is a better way. Just follow the directions above to re-season it, but let it sit in the over for 90-120 minutes. The extra time is needed to bake down the thicker, gummy stuff.
Really, almost any time I get in trouble with cast iron I'll just pop it in the oven and cook the bad stuff off. Cast iron waffle irons are really lovely and fun to learn to use, but mistakes can be hell to clean out. I just scrape as much out of the waffle pattern as I can put the waffler in the oven (remove any wooden handles, please) and bake off the failed breakfast treat. I also find the waxy, gummy buildup forms fast on the waffle iron stand.
Finally: never put cast iron in the dishwasher. Any time you get it wet, make sure you completely dry it. I put it on the stove and heat it up to ensure it is dry. While the seasoning is tough, anything beyond a few minutes exposure to water will start taking it off. If this happens, don't panic. Just re-season it.
Great thing about cast iron is the more you use it, the better it gets.