So shopping for fresh produce in zero waste style isn't too difficult. Most produce is available without packaging. Just make sure you avoid those plastic baggies by refusing plastic bags or bringing your own canvas bags if necessary.
The rule of thumb for zero waste grocery shopping is to stay in two sections: produce and bulk.
Meat eaters can also get fresh meat from the meat counter zero waste.
Check out a video I filmed at Sevananda Natural Food Co-op for more tips on zero waste grocery shopping.
A few fresh items I find difficulty finding without packaging are small fruits like berries, grapes and cherries. For the berries, I recommend a farmer's market check out this comprehensive list of farmers markets in Atlanta. For trash free grapes, go to Sweet Auburn Market, a couple of the vendors there will give them to you trash free as long as you have a reusable bag to place them into. Let me know if you have any tips for cherries.