The main thing with greens is to keep them cold, and prevent them from drying out. If left uncovered in the refrigerator, leaves will loose their moisture and wilt.
For me, this means simply throwing the greens in a plastic bag (sealed or slightly vented is fine), and storing in the fridge. Wash the greens on the way out. For a more involved process, see below...
The storage method outlined here is for Bok Choy, but can be used for just about all leafy greens. Be sure to dry the leaves thoroughly before storing!
Step 1: Cut the root of the bok choy off, where the leaves join together at the bottom. Keep the white stems of the bok choy as you will most likely be using both parts of the leaf in your recipe.
Step 2: Fill a large bowl with cool water and soak the leaves of bok choy for about 30 seconds. Swish the leaves around in the water to remove any dirt.
Step 3: Remove the leaves of the bok choy and gently shake off excess water. Blot them dry on paper towels.
Step 4: Roll out another section of fresh paper towels. Place the leaves of bok choy on the paper towel in a single layer. Roll them up.
Step 5: Store the rolled leaves in a plastic bag.
Step 6: Place the bag in your refrigerator crisper. The bok choy should stay fresh for five to six days.
This method is published online here.