I don't wash my garlic at all. I just let it dry on the kitchen counter for a couple days. Then I snip the roots short, snip the stalk off, and take off a couple of the garlic skins till I get down to a clean, white layer. At that point, they're dry and they should come off readily. You can take a dry brush (like a vegetable or mushroom brush) to the roots to get some of the dirt off.

If you peel off one or two of the leaves down to the bulb, most of the dirt comes off. Then you can snip off the roots. I tie 4 or 5 stalks together and hang in the barn to dry.

I usually get the dirt clumps off the roots and skin with my gloves at harvest. I don't clean again until I get ready to bring it in to the house to use OR take it to farmers market.I like to wait until the outer layers are dry and take of one or two paper layers it is fast and easy that way. You probably saw farmers cleaning it at market because they want it clean to sell and it is one time they may have time to clean some.

No, you shouldn't wash garlic. That will encourage mold and the garlic will not store as long, even if you try to dry it right away. Just dry-brush some of the dirt off, or peel the outer layer of skin as others have already pointed out.

Also, don't harvest it on a wet day. And stop watering the garlic location at least a week before harvest time. I am about to harvest my own garlic here in 6b. Definitely looking forward to it.