We have an iPod shuffle for my 8 year old, and what you need to do is go to iTunes.com. They have a free software that you can install on your computer. From there, you can put CDs that you already own into the disc drive of your computer and download that music into iTunes. There is also an online store at iTunes where you can buy music if you like. The songs are around $1 each and you can listen to ~30 seconds of the song first to decide if you like it, if that's the exact version of the song that you want, etc, before you buy it. You can also buy podcasts, books on tape, that kind of stuff.
Anyhow, once you have your music in iTunes, then it's just a matter of hooking up the iPod to your computer using the included USB cable (or docking station, or whatever method came in the box of connecting the iPod to the computer), and the music will automatically go from your computer to the iPod.
Now, read the directions on this, because the Shuffle is meant to play a playlist at a time. In other words, if you download several different genres of music (say, you have a Black Eyed Peas album, and some Marvin Gaye, you may not want all of that on "shuffle" on your iPod all at once). So you would use iTunes to create "playlists" of the types of music you like. (A playlist is just like the mix tapes we used to make in the 80's - remember those? =) So maybe you put your Black Eyed Peas with some Lady Gaga (just making this up for the sake of argument here =) and some Katy Perry and Madonna, and that is a playlist that you name "Workout Music." And then you take your Marvin Gaye and put that with a few other R&B artists, and you call that playlist, "Hanging out drinking a glass of wine." And then you only put one playlist on your Shuffle at a time. (If you upgrade to an iPod Nano, you can put all your playlists on there at once and choose which one you want to listen to at any given moment, but the Shuffle is more basic.)
Anyway, I hope that helps a little! Check out the FAQ at iTunes, that may help also!