If there is a market near you, sometimes when they close they let you have some stuff, such as the leaves of carrots, that they cut off. If they let you have it for free you can actually eat it, either by making it into soup or by cooking it like spinach. Actually the leaves of lots of vegetables are edible, and people tend to consider them trash, so if you can find a store or person who'd be willing to give them to you...
You can also go to bakeries and ask if they have stale bread. They might sell it to you cheaper or give it to you, and you can use it in soup or for French bread.
As far as protein goes, grains+legumes bring protein, so rice and beans or pasta and lentils for instance. You can often find them for pretty cheap.
If you're too embarrassed to ask for stuff, keep the leaves you take out when you make vegetables (if you can afford them) and put them in the freezer until you have enough to make broth. Then throw away the leaves (they'll have lost all their taste anyways) and use the broth to cook your rice of lentils, this way you'll get vitamins from the plants and the rice or lentils will taste better.
There are often sales on produce that's "too old" but with apples that look like they have gone bad you can still make apple sauce, just dice them and cook them slowly while stirring. You don't need to add any sugar or water or anything, just let them break down and then you have apple sauce.
If the stores next to you have an area where they sell stuff that's almost expired, try shopping there as much as possible, but don't by something just because it's there. Sometimes there will be stuff half price that will still be more expensive than another brand, so make sure to compare prices before you buy anything.
It's probably for the best to have meat as little as possible as it tends to be more expensive (especially fish), but legumes will bring the right amino acids so make sure to have them (beans, lentils, split peas or chickpeas, peanuts).
If you ever do eat meat pick some with bones and make broth with that.
Look carefully for promotions and coupons but always check that there isn't a brand that's even cheaper than the one one sale. In some cases, buying a lot of something is cheaper, in these cases it's best to team up with other people, buy together and split it (depending on the product stocking up can mean the product will just go bad before you use it, plus it can cost too much at once even if it's cheaper in the long run).
Never eat out and don't buy junk products, as they're more expensive and less healthy.
I survived like that for a year on almost nothing, and I'm getting low on money again so I'm getting ready to do the same again.
