Open the iTunes program on your computer, and plug the iPod cable into the iPod Nano's dock connector. The dock connector can be found on the bottom of the iPod Nano, according to the official Apple site.
Plug the other end of the USB cable into the USB 2.0 port on your computer, and wait for iTunes to display the iPod Nano icon in its source list. The source list is commonly known as the sidebar, on the left of the program window.
Select the "Music" tab next to the "Summary" tab in the iTunes window, and check the box next to "Sync Music." Select "Entire music library" to transfer your entire iTunes music library to the iPod Nano, or click the "Selected playlists, artists, and genres" to automatically sync specific items to the iPod Nano.
Check the box next to the music you want to transfer to the iPod Nano, and click the "Apply" button at the bottom of the iTunes' program window. The synchronization status will appear at the top of the iTunes window, and will display a disconnection message once the synchronization process is complete.
Remove the USB cable from the iPod Nano's dock connector.
Run the iTunes program on the computer, and plug the iPod cable into the iPod Nano and the USB 2.0 port on the computer.
Click the iPod Nano icon in the iTunes' source list, and check the box next to "Manually manage music and videos" in the Summary section of the iTunes window. Select the "Apply" button to switch the iPod Nano to manual mode, and click the Music tab in the iTunes source list.
Drag and drop the songs from the Music section of iTunes to the iPod Nano tab in the program's source list.
Click the eject button next to the iPod Nano tab in the source list to manually disconnect. The eject button is the up arrow on the iPod Nano tab.