How should we handle shares when co-founder leaves?

Absent any provision in your charter documents (if you have them) that identifies buyback or other transfer protocols, you are defaulting to your state's Corporations / LLC Act to see what your respective rights and obligations are. Is the co-founder pressing you to buy him/her out? Do you want to? A basic option would be to agreeably value the business and simply buy his shares. Alternatively, the business could buy his shares back and cancel them. There will be some tax implications for your person and the business depending on how you want to handle it, but any actionable advice will require more facts. You should speak with local corporate counsel.