Here are some tips.
Farmers markets and other market like places can sell produce cheaper.
Know prices store to store and buy on sale
Eat veg. In season
Some veg. Can be literally grown in a pot in your house/apartment herbs too
If veg. Is on sale buy it and freeze the excess for later date.
Have a food party if you have time ( grab a few friends each cooks a dish for the amount of people joining, everyone brings containers and you have a few meals)
Make a few meals and freeze to have "instant meals" during the week.
Eat less meat and fish (either decrease in size and/frequency)
Buy dried before you buy canned ( dry beans are cheaper then canned) industrial canned foods are not that good for you.
Learn quick/cheap/easy dishes from other cultures
Learn how to can and pickle at home ( basics for canning are jar,vinegar, pot and hot water)
Bring your lunch and snack for the day with you.
Instead of buying juice , if you can afford a soda stream you can make syrup for your own soda that will have less sugar or even none. (Ex . Boil ginger,strain , add sugar,cook and then add
seltzer) , make tea or lemonade.
You can make your own granola brith oatmeal too!
Decrease your amount of starch but up your veg intake.
General portion control as well, including eating from smaller dishware . Teach your self to eat more slowly too.
If you have time join a community garden, not only people give you free stuff some times, many things can end up being cheaper.
Smaller shops sometimes discount produce if it looks ugly or if it is mid day and they have been there since the morning.
Explore other fruits and veg too. (Sometimes they can be cheaper)
Just doing a few of these thing helps... I'm not saying to do all but these are things I have done to cut costs at point or another.