iPod won't appear

If the shuffle is brand new, make sure the docking cable plug is completely inserted into the shuffle's headphones jack, as shown in this document

http://support.apple.com/kb/ts3572

If that's not the problem, did this shuffle previously work properly with this Mac, and does not now for some reason? Or is this the first time you are trying to use this shuffle?

As a test, shut down (power off) the Mac and disconnect all USB devices (you can leave standard keyboard/mouse connected if used). Do this to Reset the shuffle

http://support.apple.com/kb/ht1655

Start up the Mac, run iTunes, and connect the shuffle to a direct USB port on the Mac.

If your Mac is a recent model with USB 3.0 ports, as another test, if you happen to have an older USB 2.0 hub that has its own power supply, connect the hub to the Mac and connect the shuffle to the hub. Does that make a difference?

When you previously used it, it was with this Mac that you are using now?

So, it does not appear in iTunes, in the sidebar under DEVICES? NOTE: If the iTunes sidebar (along left side of window) is hidden, from the menu bar, under View, select Show Sidebar.

If not, quit iTunes and run Disk Utility. Does the iPod appear in the Disk Utility sidebar, in any way?

If not, select About This Mac from the Apple menu, and click More Info. Do a System Report, and look under Hardware - USB. Does the iPod appear listed as a connected device?

Also, keep in mind that if the shuffle is less than one year from purchase date, it is still under the standard warranty.

If you have an Apple Store nearby, you can make a reservation at the store's Genius Bar and take it there. Usually, Apple uses the iPod's serial number for warranty coverage.

If you take it to the Genius Bar, be sure to bring your USB docking cable. It is possible that the cable is faulty, not the shuffle. If your Mac is a MacBook, you may want to bring that along too.