This is something I'm starting to worry about.
Right now, I'm fine. I'm a college student who works usually around 15 hours a week. One of my two jobs is working as a prep cook in the kitchen, so this means I get free breakfast and lunch on the weekends, along with any leftovers I want to take home when there's something good (tofu scrambles, rice and bean dishes, veggie stir-fries), so I save a decent amount from this. I also am close with a lot of the kitchen staff, so I can pretty much get onions, peppers, salad greens, etc. whenever I want (I don't like abusing this ability though).
I have a small meal plan for 7 meals a week, which usually means I get lunch in the dining hall during the week days and dinner on the weekends. I also can get free breakfast every week day since the meal-checkers are really relaxed.
I've definitely been taking this for granted.
This summer, I'll be interning with a biologist and received a grant which basically pays me minimum wage. I get it in chunks after writing up reports updating the administration on my progress during my internship. A little bit more than a third of the money will go to rent and bills. The rest I need to ration on groceries, bus fare, train tickets to visit my family, rabbit supplies for the bun, and art supplies. It's going to be tough, but I definitely plan on going to the farmer's market as often as I can, maybe joining a CSA?
The past two summers, I also worked on my school's small farm, so I'm used to getting produce for free during the summer months. I'm still working through the garlic harvest! I've been so spoiled!
The grocer a town over from me has a sale rack in the back where they sell food that is about to go bad. I managed to get a pound of grapes for only 80 cents and 5 bananas for 30 cents the other day!
Potatoes are also a great way to get a nutrition-packed veggie for cheap. Obviously, there not great to eat every meal or even every day, and should be steamed, but it helps stretch the budget.
Foraging is also great if you live in a place where you can. Dandelions, clover, and plantain are all edible, nutritious, and free. If you can't spend the $4 on a bunch of kale, it's a nice way to add some dense-nutritional greens to other dishes (but wild dandelion can get pretty bitter, so it takes some force to chew it down). They should also be washed really well and shouldn't be picked if there growing near a road.
Buying in bulk always helps. I'm planning on stocking up on oats, rice, pasta, dried beans, lentils, and couscous before I move at the end of the semester.
And if there's ever something healthy on sale, buy a ton! You can always freeze berries, steam veggies to then freeze, or make a lot of a meal and store it in serving-size containers in the freezer so you have ready-made meals from on-sale groceries or things that were going bad.
I don't eat animal products, so that makes my expenses a little bit cheaper (especially since I would never eat industrially raised animal products for a variety of reasons). Cutting down on meat consumption will cut down on money. Beans are cheaper and can help stretch dollars
I hope this helps!