I used to think this until I started eating healthy. Now that I really know how to eat healthy, I spend about 1/2 of what I used to on groceries. Think about eating more simply. Today, we had baked potatoes with homemade vegan chili on top. Soups are great inexpensive, easy to make, and healthy meals.
Use rice, beans, lentils, etc. instead of meat in lots of dishes. We buy all our fruits/veggies from a local food co-op called bountiful baskets. The produce available there is so much higher quality than what is available at the grocery store and costs about 1/4 as much. So, look into your local food co-ops. If you do an online search, you should be able to find out what's available.
Learn to make your own bread type products. We make all our own bread, buns, tortillas, etc. It's all 100% whole wheat and healthy. It costs me far less to do that than buy at the grocery store. (about $0.50 for bread or 12 tortillas)
Eat some hot cereals (such as oatmeal or cracked wheat) for breakfast. Cold cereal is really expensive and not very good for you. If you buy a huge bag of regular oats and cook it up for breakfast, it will fill you up and be a great healthy meal for hardly anything. I also know what I am adding to it. Those little packets of instant oatmeal at the store are full of all kinds of stuff that's just not good for you. Add a little honey or agave and some frozen fruit to the oatmeal and even your kids will think it's great!
Brown bag lunches. Try chopping up chickpeas with mayo instead of chicken or tuna salad on bread for a great sandwich. It's better for you, tastes great, and costs MUCH less. I can buy a large can of chickpeas at
Walmart for $0.65. It makes about 3 times as much as a can of chicken or tuna, costs less, tastes great, etc.
Hope this gives you a few ideas. Focus on learning one new thing at a time. Make a few substitutions with your regular meals. It took me years to get where I am now, but am very pleased with the results.