You run iTunes, and click on iTunes Store in the sidebar. Log in using your Apple ID (iTunes account). On the main iTunes Store screen, along the right side click Redeem under Quick Links.
On the Redeem screen, enter the code from the gift card. You should then be able to use the "credit" in your iTunes account to buy (and download) songs.
Once the songs are in your iTunes Music library, you can sync them to your nano.