Once you are inside, start with the produce and end with the frozen foods. Save your grocery shopping until dinner hours or after nine o'clock. The lines are definitely shorter. You can also try going before or at seven in the morning. Depending on the grocery store, you can find special deals early in the morning.
Coupons do save money.
Whenever you see one, clip it and store them. For better organization, keep a coupon binder. In the binder, put pouches with differing labels on them. When you find a coupon, just stick it in the appropriate pouch. When it's needed, it'll be available for your use.