Kosher salt and a small amount of vegetable oil. Scrub the pan with the salt on a rag or paper towel, if there are stubborn bits mix a couple drops of oil with the salt, wipe dry with clean towel.
If you use a wet method to clean the pan re-heat it after cleaning to make sure it is completely dry before storing.
cooking.stackexchange.com/users/51/Janelle
Besides what @Janelle said, for really stuck on stuff, use a similar process as you'd use to deglaze the pan --
While the pan's still hot (or heat it back up if you've let it cool), and then add some cold water.
Some should instantly steam, and should hopefully be hot enough to boil a little. (don't add so much water that you cool down the pan).
Scrape the bottom (I use a wooden spatula), dump out the water, and if there's still lots of stuck on bits, repeat.
Wait a minute, dump out the rest of the water that's puddled up, and wipe with a paper towel to dry, let any remaining water evaporate, and then a quick coat of oil before putting it away. update :
per comments from event_jr : this technique may not be safe for carbon steel pans.
cooking.stackexchange.com/users/67/Joe
Another alternative is to go to an East Asian grocery and pick up a wok cleaner, which looks like a tiny little broom made of stiff sticks.
It does more-or-less the same thing as the coarse salt.
I find it particularly useful for cast iron grill pans, as it's easier to get leverage on burnt-on material than when using salt.
It'll cost you maybe two dollars (US).
cooking.stackexchange.com/users/45/Harlan
We use tap water + a cheap plastic-bristled kitchen scrub brush to get all of the food bits off.
Then put it on medium heat on the stove until it's dry.
The heat will sterilize for you.
Why medium heat?
Someone told me it's better for the pan than using high heat.
It sounds logical but I have absolutely no real proof.
cooking.stackexchange.com/users/43/Dinah
I run mine under cold water and gently scrub it with a brush to remove any large stuck-on bits (it's well seasoned, so nothing really sticks to it).
Then I stick it on the stove on high and when it's good and hot, I rub it down with a paper towel that's been dipped in Crisco or vegetable oil.
This kills any germs, removes any fine bits that might be stuck, and re-seasons the pan.
Run the paper towel under water before you throw it out.
If you don't, the resulting trash can fire will make you feel stupid, if not worse. :)
cooking.stackexchange.com/users/2042/Dave
Pretty much same as all else.
Wash with only a brush and hot water (while the pan is still hot) to get residue out.
Except when I have fried something that will leave a taste, like fat fish (salmon, herring or similar).
Then I also use dish-washing liquid along with the brush.
Dry off on the stove after cleaning with water.
The thing to remember is that cast iron will contain small hollows which should contain fat.
Otherwise everything will just burn.
Feel with a finger if it "feels" fat.
Otherwise pour on some cooking oil and let it simmer in low heat for a while.
Swipe off excess with a paper towel. /L
cooking.stackexchange.com/users/176/leiflundgren
I have a seasoned cast iron skillet, and I don't want to mess up the seasoning when I'm cleaning it.  What do I use and what don't I use to get it back to clean?  I've heard not to use soap and to make sure it is dry, but nothing beyond that.
How do you clean a seasoned cast iron skillet?
cooking.stackexchange.com
<equipment><cleaning><cast-iron><maintenance>
cooking.stackexchange.com/questions/261
cooking.stackexchange.com/users/63/plor
A well-seasoned cast iron pan should be easy to clean with a brush and hot or cold water. Kosher salt can also be used, with some added oil on stubborn parts. Deglazing is also effective. You can simply use water and a brush to scrub off any food residue. You can also use salt and a little oil or a deglazing technique before rinsing.
Scrub the pan with salt and a little oil to remove residue. Use water and a brush while the pan is still hot. Deglaze the pan with water and rinse.