Why is the "sync" option greyed out in my iTunes?

I just downloaded iTunes onto my old computer so I could get all my old music onto my iPod nano. I finally got all the old stuff into my iTunes library… plugged in the iPod, and it won’t sync. When I go to File > Devices, the “sync” option is greyed out.

I don’t know if I’m stupid or if Apple is needlessly difficult, but I can’t see any reason why the iPod won’t sync. Can someone help me here? I’m ready to throw everything out onto the lawn.