Hello there!
I looked up the specs on the Nano and it can be powered by placing 7-12 volts on the "Vin" pin and Ground on the "G" pin. Your 9V battery certainly meets this expectation.
Below is a picture of how you can power the board, as well as a snippet from the specifications page. All you would have to do is cut the small barrel from the end of the 9V battery snap so that the two wires are showing.
