There are two things you should have with you, your list and your coupons. Pre written grocery list and pre sorted coupons will save you tons of time at the grocery store.
Fast Trips: Run in with the coupon you need (if any) in hand and get the quick pre selected items you need by going promptly to the isles containing those items. Do not browse. Remember this is only a fast trip.
Grocery Shopping: Start at one end of the store and work your way through each isle slowly to till you reach the other end of the store. If you buy bulk buys, hit the isle that contain the big bulk items first to make sure you can place them safely in your cart. Now, take out that list and as you browse through each isle keep in mind what you are looking for. As you find the item cross it off from your list and (if applicable) pull out the corresponding coupon. By pulling the coupon for the item you place in your cart you will save time at the check out counter. You can safely keep the coupon separate by clipping to your list.
At the register you can now unload your groceries, put away the coupons you didn't use and have ready those you did for the clerk.