First of all, as much as possible, I use a straw mulch under all greens. this includes, leaf lettuce, romaine lettuce, spinach, chard, kale, cilantro and parsely, turnip or beet greens, too. The straw keeps most of the dirt from splashing up on the leaves in the first place.
Then, I harvest when they are ready. I might snip them leaf by leaf, or cut the whole plant for something like cilantro or head lettuce.
Then, the harvest gets brought inside for washing.
The best way I have found is to take a large bowl, fill it with cold water, and place enough of the greens to be under water, so you can swish them around. Handle tender greens gently, but move them around in the bowl of water to loosen any dirt. Let the water settle for about a minute, then carefully take the greens out and lay them on a dry towel or paper towel. you should see debris or sand in the bottom of the bowl. Toss that water, rinse the bowl, and repeat this process until there is no more grit coming off the leaves. I usually wash three times. This works better than trying to rinse the leaves under running water. Dont ask me, it just does.
Once they are rinsed, use a salad spinner to dry them. I am not big on kitchen gadgets, but a good salad spinner will really get the excess water of your greens. And moisture will cause them to deteriorate faster in your frig, so the drier you can get them the better.
Then, put the leaves in your container of choice, a ziplock bag, or plastic tub, whatever.