iPod is not Charging
Start with force restarting your iPod Shuffle.  If that doesn't work there are three things you need to check:

The USB port is functional.  Try another device (any device is fine).  If it works, then you know your USB port is working.  If it's not, then you'll either need to use a different port (if available) or another computer

Check the cable.  The USB cable may be damaged and no longer allows for communication between the iPod and the USB port.  If possible, borrow one from a friend (preferred method), or you may have to purchase another one.

Verify that the Shuffle works.  If you can't get it to work (i.e. play music) then you definatley have a problem with the iPod.  If it will not communicate on the USB port, it's likely that the iPod USB interface has died.  It's unfortunate, but it does happen.