Cast iron has a reputation for being demanding that it does not really deserve. There are exactly two rules, and everything else people tell you is either a consequence of them or a myth that outlived its cause.
Do not let it sit wet. Do not put it in the dishwasher. That is the whole of it.
The daily routine
Clean the pan while it is still warm — residue lifts far more easily then. Hot water, a stiff brush or a chainmail scrubber, and dish soap if you want it. Then dry it properly, which means a towel followed by a minute on the hob until no steam rises. Finish with a few drops of oil rubbed over the cooking face and buffed until the pan looks dry.

Stuck-on food
The instinct is to fill the pan with water and leave it. That instinct is precisely what rusts pans, and it is unnecessary — a hot pan releases stuck food faster than a cold soak does.
- Simmer water in it. Half an inch, bring it to a boil, scrape with a wooden spoon. Everything lifts within a minute.
- Coarse salt. A tablespoon and a folded paper towel makes an excellent non-damaging abrasive.
- A metal pan scraper. A few pounds, and better at this than anything else.
- Chainmail. Ideal for burnt-on residue; it removes carbon without cutting into seasoning.

Rust is not the end
A rusted cast iron pan looks ruined and essentially never is. Rust is surface oxidation on iron that is at least several millimetres thick, so scouring it off costs you nothing structural.

Scour back to bare grey metal with steel wool, or soak in a 50:50 vinegar and water solution for no more than an hour — vinegar keeps eating iron once the rust is gone. Wash, dry hard (bare iron flash-rusts within minutes), then season three or four times.
The full seasoning method is in how to season a cast iron skillet.
Reading the symptoms

One symptom worth calling out: black residue on a paper towel after wiping. Almost everyone assumes this is seasoning coming off. It is loose carbon from cooking, it is harmless, and it stops after a few wipes. Seasoning does not transfer to a cloth — that is the definition of a cured coat.
Storage
Store it bone dry with a trace of oil on it, and put a paper towel inside if pans are stacked or if the pan lives somewhere humid. If it has a lid, store the lid off or ajar so moisture cannot be trapped against the cooking surface.

The short version
- Clean it warm, with hot water and a brush. Soap is fine.
- Never soak, never dishwash, never air dry.
- Dry on the hob until no steam rises, every single time.
- Wipe on a trace of oil while it is still warm.
- Stuck food: simmer water and scrape, or use salt.
- Rust is recoverable. Scour, dry, re-season.


