I season mine on the stove top. I let it heat dry, then add a drop or so of vegetable oil and wipe around the bottom and sides. Continue to let it heat with the oil in it for 15 - 20 minutes.
When I wash mine...yes I do too...I wash with dish soap and hot water. To dry it I place it back on the burner and let it get hot until the water evaporates, then I wipe it with oil on a paper towel again. I've had the same set of skillets for over 30 years and still counting.