How do you clean your cast iron skillet?

I have had a cast iron skillet that's basically been in continual use since at least the 1930s. I'm not fussy with it. I scrub it with a plastic scrubber and dish soap, dry it well either in the oven or on top of the stove, and oil it a bit after every use. This is the routine I've followed with this pan since I inherited it more than 40 years ago, and it has no rust and nothing ever sticks to it.