Protein, fibre, and low fat, although you need some fat. Critical shopping is a lot of it. Make careful comparisons between the what's in the produce section and the same thing canned. Often, the effective weight of useful product can be less expensive in the can, especially in the off-season. When you're trying to stretch, you'll find that a little bit of meat in a dish is as satisfying as when it was a big part of the recipe, and the cheaper cuts taste just as good, often better.
Trimmings go into the next day's soup stock.
I think a lot of it is working up recipes in enough variety that you don't start to feel down and out because you're trying to eat cheaply. Check all the prices on all the produce every time you shop. You can go along assuming something's always one price, without noticing that one day it's priced very low, either because they got a deal, because it's in season, etc. And they also can be chopped and frozen for additions to other dishes. Making your own cookies is much cheaper than buying a package of decent prepared stuff.