When I fry in mine, I deglaze the heated pan with cold water, and use a turner and/or a brush to loosen all the fund in the bottom of the pan. If what was cooked has a sauce or liquid, I spray it until free of what I cooked, and wipe it with a paper towel.In both instances I wipe out all the water and loose stuff, then spray with olive oil and wipe it out to leave a velvety black finish.
Don't forget to hit the bottom of the skillet with a bit of oil and a wipe if it even thinks about rusting.
I only use soap in mine if I have a lot of residual grease, and don't want to plug the plumbing. No brush or serious scrubbing, just let the soap emulsify the grease and pour it down the drain with hot water.