How do I run a report for tips and donations collected or tracked by TipGenius?

The Tip is tracked as a product, so you can run reports in your Analytics/Reports section (e.g. most commonly, the sales by product report). 

For a list of customers that have donated, it may be easier to do a search for the tip product (e.g. "Tip" in your orders, or based on whatever you've named it) in your orders page and export that list. This would have the customer email associated with each order, and all the donation amounts per order as well. Here's a relevant thread for reference.