Green Onions (aka Scallions) are just immature onions. You can eat the whole thing, but the real treat is the green tops.
HOW TO STORE: Open bag in the fridge, ideally high humidity. If they start to wilt soak them in some cold water to liven them back up (root end down in the water).
HOW TO USE: Use whenever you want that onion pop, without the peeling and cooking. You can cook with green onions, but they are great fresh and have a sharp onion-y flavor yet it isn't so overpowering that you can't eat it raw. If salads are your thing they make a great veggie addition.