Get a store savings card if your store has one.
Plain a shopping list before you go to the store.
Also eat before you go to shop you will not be temped to buy extra things as easy.
Shop from the back of the store to the front to avoid the stores eye catchers.
Take a calculator and round everything up if it $1.50 make it $2 this will keep you on or even under budget.
By store brand when you can and if it costless, and taste good.
Look at the sales ads to plan your list. If you shop at wal-mart they price match if you have the ad with you.
Get coupons for items you use.
For fruit and veggies it is cheaper to buy them whole then it is to buy a bag of say like salad. As frozen can save you money when fresh food prices or high.
in summer shop at your farmers market, you will save a lot by doing so.
If able buy bulk and freeze, like onions you can chop and freeze then use them in cooking, just not as fresh because they go soft.
Shop the day old rack. most stores have them. you will find bread, cakes, and other items that you might need.