It can be irresistable to wear something new right out of the package.
But unless they're fancy stockings or handmade they probably should be washed before you wear them. I'm going to use our newest & softest version for this demo, but our shorter & longer versions use a rougher crinoline that benefits greatly from a washing or two. I start my machine with cool water on the gentle cycle, add in my detergent, you could use a gentle brand or one designed especially for lingerie, I use the one that smells like lavender from Trader Joe's. Then put the petticoat in right around the center post, add fabric softener if you like (baking soda is a nice natural option).
After the final spin hang it over a towel or from a hanger outside to air dry.

You could probably get away with a low setting on the dryer if you're in a hurry, but I like mine air dried, the lace will look nice longer this way ~:)