How do I make "Store Pickup" available in checkout?

Store pickup is a shipping method, so you can activate it the same way you manage other shipping methods (see How to manage shipping methods).  

Store Pickup is within the "Manage Shipping Methods" button on the Generic carrier tab when editing a distributor.  Simply check the "Active" checkbox in the store pickup row and click Save Changes to have Store Pickup display as an option when a user is ordering a product from the distributor you're editing.