All one really needs to properly gather wild edible plants is sharp knife, a digging tool, and a container to hold your harvest. Personally, I prefer to use a garden shears instead of a knife when gathering leaves, shoots, tendrils, twigs, and other items that are cut off a plant. Note though that I always have a knife with me as part of the 10 Wilderness Essentials. For digging roots and tubers I use a Japanese Hori Hori Knife.
My harvest container depends on what I'm collecting. A net bags such as the type onions come in is very good for leaves/twigs/roots. Reusing a bag like this is also good for the environment. Berries and other delicate plant matter work best in shallow Tupperware-style containers. Don't use high-sided container for berries. You'll be tempted to fill the container to the top and the resulting weight will crush the berries at the bottom.
A bag with lots of pockets works great for carrying your tools, guidebooks, and harvest containers. I prefer a shoulder bag to a backpack because the shoulder bag has quicker access. You need to remove a backpack to take out/put in stuff. Shoulder bags do have an annoying tendency to swing forward into the way when you bend over, but I find clipping it to one of my rear belt loops with a cheap carabiner takes care of this problem.
Other optional gear:
1. Guidebook of edible plants (better safe than sorry)
2. Leather gloves (some plants have thorns)
3. Sunblock
4. Bug repellent
5. Long pants (better protection against bugs, sun, thorns, etc...)
6. Water (duh)
7. Small notebook
8. Ruler or small tape measure
9. Camera
Buy my book! Outdoor Adventure Guides Foraging covers 70 of North America's tastiest and easy to find wild edibles shown with the same big pictures as here on the Foraging Texas website.