You really have to shop with meals already in mind - a plan on how to use them. (This diet takes a lot of organization). Some veggies naturally go bad before others, so eat or cook those sooner in the week rather than later. If you can't get to it, try freezing it!
Also so very important to pay attention to the sell by dates on the proteins you buy. Same thing, just freeze it and thaw it later if you can't get to it in time.