Wash the nylons gently, I use a metal or ceramic bowl, not the sink.   Avoid rubbing and pulling.   This will stretch the stockings out of shape and could start a 'run'.   Extract water by gently squeezing stockings.   Do not slide your hands up and down the stockings.   Lightly squeeze them to remove excess water.   Use cotton gloves if you don't manicure your hands.   I use a emery board on my nails and rough spots on my skin of the fingers.   Lay on a towel to dry.   Or hang the stockings gently into shape, feet down, on a cotton towel draped over a shower rod away from high heat and direct sunlight.   Never put in a washing machine or dryer.  

Do a good pedicure.   Use hand lotion on the feet and legs to make your skin smooth and sexy.   Use gloves to put the stocking on to keep from sag them with a finger nail.   I have ironed new ones that were rumpled in the box. I set the temp to the nylon setting, once they cool to room temp the color comes back.   The soap should be mild and very diluted to keep the acidity low so that the dye doesn't leach out.   After hand washing I use a hand lotion on my hands to keep them from drying out.  

Store them in plastic sandwich bags, one pair in one bag.   For heavy stained nylons, you know what I mean, I have soaked overnight in very hot water and heavy soap.   This seams to dissolve the stain pretty good.   But you do notice the dye leaching.   So, put both stockings together for this treatment, so they'll match shades.   To stop a run from getting longer, I carefully put my hand inside the stocking to get one finger under the end of the run.   Then I put a small,SMALL dab of clear finger nail polish at the end of the run.   I let it dry by moving my finger away and breathing on the spot for a minute.  

I'm trying to think of anything else to tell you.   I think that this covers every thing, except for dying the light colored stockings. It is really messy.   I was never happy with the results.   The water temperature, dye concentration, time, all have an impact on the outcome.   I've learned to appreciate the subtleties of the shades and hues in stockings from one batch run to another.   I used Rit dye black.   I'd end up with strange hues of blackish purples.   You really need to start out with washed white nylons.