You can wash it like almost any dish but avoid abrasives... this no washing with soap rule stems from the days when soap contained lye which is the best thing for stripping old cast iron.

I give mine a light scrub and a rinse as very little sticks to a well seasoned pan and then give it a light coat of vegetable oil to protect it.

The smaller #3 skillet is going to take a little more work to bring it back to what it is supposed to be... this is a great size for a single breakfast or making bannock so it will get a lot of use.