Taking care of a cast iron skillet isn't as complex as it seems.
When washing the cast iron skillet just avoid using steel wool, soap or the dishwasher to prevent damaging the cast iron skillet.
Just washing it with some water is usually good enough to keep it clean and if something is stuck on it you can scrub the cast iron pan with Kosher salt and water.
You also need to season the cast iron skillet periodically and to season a cast iron skillet all you need to do is heat the cast iron skillet up on the stove until the skillet is smoking hot and then rub a little vegetable oil into the cast iron skillet and then just let it cool down and the oil will season the cast iron skillet.