For our family the first thing we targeted was juice and drinks. Starting there, you can save a lot. You don't need coffee, and especially not starbucks, or Monsters, or soda pop, etc. If you do fast food, skip the drinks, and ask for water if you really need something. The drinks are usually unhealthy, so if you calculate the true cost of soda pop for example (including the eventual dentist bills), it's pretty expensive, even if it seems cheap.
Second thing to target is food waste. We were really having a problem with food going bad because it would get "lost" in the back of the fridge, or we'd lose interest in those breadstuffs and they'd grow moldy.
Another thing you can try, it's inconvenient and I have not yet done this on a regular basis, but have an envelope where you put allocated food money from the budget. When you shop for groceries use the cash, not a debit card. You have two things working for you: 1) you can't spend more than you have in the envelope, so it forces you to stick to the budget, and 2) they say when spending cash rather than a debit card people have a much easier time saying no to an impulse and hanging onto the cash. You really feel the outgo if it's cash, and you don't if it's on a card.
Here's another insight, and we have just started doing this: try to have a designated shopper. I can't count the times that I bought a few groceries on the way home only to see that my wife had done the same thing. we bought different things but we were buying more overall than we needed. Decide between you whos doing the shopping, and eliminate those surprises.
Last one. We find that if one of the kids needs something and we have to take time out of our day to go to the store, it's hard to not buy ourself something too. For years I did this till I started to see what I was doing to myself. If my daughter needed something that cost $10 then I'd get myself somthing too, because "why should she get everything?" Now I try to tell myself if I really must go get something for the kids, I don't "treat myself" which also make it easier not to let the kids add a treat for themselves to the purchases.