Nylons tend to be more expensive than their lycra counterparts and you want to get the best possible wear out of them.
Nylons will last longer if given a gentle handwash in mild soap and lukewarm water - they are going to get snagged in the washing machine unless you use a lingerie/hosiery bag, but the wash cycle is also tough on the delicate material.
After handwashing, rinse thoroughly in cool water and roll in a towel to remove moisture.
Dry nylons at room temperature.
Storage should be in a smooth sided container. You might also wrap individual pairs in tissue to protect further from snags.
You can also prolong the life of nylons by 'resting' them - so alternate wears of several pairs of the same colour will give you much better wear of all of them than if you just wore one pair until they needed replacing.
The other advantage to having several pairs of the same colour is that if disaster does strike and you snag one, you can still continue to get use out of the other one by alternating with other pairs.