One of the easiest things to do, for anyone, is to switch from plastic bags to reusable!
I always keep a couple folded up in my rucksack, and if you know you are doing a big shop – the more the better!
To go even further than that you could buy some brown paper bags and take them when you go shopping for veg, and use them instead of the plastic ones provided by the shop! (Or shop at your local green grocers, and they will probably supply them).
Alternatively you could use old veg boxes and crates.