iPods (that are not iPod touch) are associated with an iTunes library, not a particular Apple ID. Your iTunes Store account (your Apple ID) is separate. You can use an iPod even if you do not use the iTunes Store and therefore have no Apple ID.
When you connect it to your computer for the first time, and run iTunes, it should ask you if you want to sync the iPod to your iTunes library, erasing the current content. If you accept, the iPod will be associated with your iTunes library going forward.
If you decline, the iPod gets set to Manually manage music. To set it to sync to your iTunes library, select the iPod in the iTunes sidebar under DEVICES. Over to the right, go to the Music tab. That screen defines how you want iTunes to automatically sync the iPod to your iTunes library. When you set it up to sync music, and click the Apply button, the iPod will be associated with your iTunes library going forward. Existing songs on the iPod will be erased and replaced with songs from your iTunes library, based on how you set up the Music tab.
NOTE: If this is a 1st or 2nd gen shuffle, it works differently, so please post back. This article about iPod shuffle syncing lists the four types of shuffles (and provides more information).
http://support.apple.com/kb/HT1719