The best way to clean a cast iron skillet is to use some hot water and a sponge or even a stiff brush.
Avoid using steel wool or soap on the cast iron skillet as using steel wool or soap on the cast iron skillet could strip away the seasoning on the cast iron skillet.
If you have food stuck on the cast iron skillet you can use a stiff brush and some paste made of some coarse kosher salt and water.