Harvest the nuts in late fall, using the heel of your boot to remove the green hull. Pick the nuts up with gloves as they stain.
For large batches, you can put the nuts in a 5 gallon bucket, cover them with water and stir with a paint or mortar mixer drill attachment to remove the hulls.
Washing
Wash the nuts until the water runs clear
Drying
When the nuts are clean, lay them out to dry, without putting them in a large pile, in a ventilated area. They'll dry up to twice as fast with a fan blowing on them. A garage works great.
Storing
Once the nuts are dried, they can be stored for years for use as a food. You can test a walnut to see if it's done by cracking some, the nut meats should be loose in the shell. Freezing black walnuts after cracking.
Video
Notes
Can you compost black walnut shells?
Black walnuts contain juglone: an alellopathic compound that inhibits the growth of other plants, meaning they should not be composted. Instead, leave the shells out for wildlife, throw them in the woods, or bring them to a yard refuse site.