Cast iron is very similar in materials and maintenance to carbon steel, so it's best to clean them both the same. Here's the quick summary: After letting your pan cool off, clean it with a brush or scrubber. After drying the skillet, apply a bit of oil to it and then heat the skillet on the stove. Use a cloth or towel to apply the oil to the inside of the skillet to retain the seasoning. Here are more instructions.