How can I delete icons from the 6th generation iPod nano?
Update: With the new update from Apple (v1.2), it is now possible to remove icons that you don't use, and to change the size of the icons.  Under Settings->General->Home Screen you can show/hide individual icons.

I don't believe that you can delete the icons.  You can rearrange them.  I moved the ones I'm not interested in to the last screens so they are mostly out of the way.  

The User Guide explains how to do this.