I cap the end of squash with some foil and that keeps in the fridge for a while. I just slice off circles of it as needed.
For green beans I put them in a reusable mesh produce bag from the grocery store and put that in the crisper at the bottom of the fridge.
I break down greens as soon as I get them home. I wash them, cut them into manageable pieces, and put them in a quart size ziploc with a folded over square of paper towel. I push the air out of the bag, mark the date on it, and put the bag(s) in the fridge. They usually last a few weeks that way and stay nice and crisp.