Basic Cleaning
Keeping a cast iron pan clean is pretty simple. The only thing you want to keep in mind is that you just don’t want to use anything too sharp that will dig into the surface, and I also don’t really suggest soaking them.
The one things that is priceless is a scraping tool. Lodge, for example, sells plastic scrapers built for this. They are just the right hardness, cheap, and quite durable. What you’ll want to do is let your pan cool down and the scrape as much food off as you can with a scraper. This should take just a few seconds. Just a warning, don’t scrape while the pan is still hot. This tends to melt the scraper. They also sell a chain-mail type scraper that can work well. It’s a very hard scrubber, but the edges are all rounded off. You can also get a hard bristly brush that works well.
Next, you can wash your cast iron with a mild scrubbing pad, bristle brush, or scraper. Sometimes I will use soap if there is a flavor I want to be sure doesn’t stick around in the pan. Just make sure you season the pan (wiping some oil on the surface and heating back up for a few minutes) and you will be good.
If you’re using water you will want to make sure to remove all standing water from the pan to avoid rust. This can be done with a towel and some oil, or simply just heat your pan back up for a few minutes (more info here). Whatever works for you. To be clear, you don’t even want water beads on the pan. That is enough to cause some rust spots.
Above all, just make sure you wipe some oil on your pan after cleaning and there will be no problems.
Note on oil:
You will want to use a high-heat oil. Extra Light Olive Oil, Safflower Oil, Grapeseed Oil, Flax Oil, or any hight heat oil is a good option. You want to use a high heat oil as otherwise a lot of smoke will be produced when cooking. You want to use enough to cover the pan with a super thin film but not enough to produce any pooling. You’re basically wiping out as much excess oil as possible.
Cleaning Methods to Avoid
Avoid using any harsh chemicals. I try not to use any metal scrapers unless it’s really needed. You can use some hard scrapers but you will need to take extra care of re-seasoning. Avoid the dishwasher. Worst case scenario though, you will just have to re-build the seasoning.
What if my pan rusts?
If the pan rusts, you should still be able to save it. Several manufacturers sell rust erasing tools and there are other methods as well. I’ve never really ran into this issue because I’m diligent about re-seasoning after every use but just know that you can still save your cast iron pan. There are many cast iron restoration communities on the internet that do incredible work.