One question we get fairly regularly from new iPod owners is, "How do you download music to an iPod?" Downloading music to your iPod is actually pretty easy. The first step is to connect your iPod to your computer with the supplied USB cable. After a moment, the computer will recognize it and open iTunes. If you don't have iTunes, make sure you download and install it first. You can download iTunes here.
Once connected, you should see a screen similar to the one below. Presuming your iTunes has your music already in it (if not, see below), select "Music" from the top of the left column. This will bring up your music library.
From here, just click and hold on the song you want, and drag it over to the iPod icon in the left column.
If you want to transfer several songs, you can Shift-click to select multiple items. If they're not next to each other, you can use Ctrl-click to select multiple non-adjacent items.
After a few moments the song or songs are now on your iPod.
If you don't have any music on your iPod or on your computer yet, check out the related topic: How to Download MP3 Music.