Coupons are a great way to save money, but stores also give great sales too!
The first tip that I would give is to go through the weekly ad for your supermarket and make a shopping list of everything that you are going to buy. Make sure you only buy items that are on sale (unless you absolutely need something) and stick to your shopping list!
The second tip is to look over your shopping list and look for coupons that match your items. This way you are only buying items that you need and will be able to save even more on them. Coupons can be found in your weekly Sunday newspaper, at coupons.com and other coupon websites as well.
The most important tip is to have fun with grocery shopping, look at it as a challenge to save money!