Q: nano won't sync

Based on that rather limited info, it's hard to guess at actual problem.  Here's some basic info, which may help...

In current iTunes, click the device button to access the iPod's Summary settings screen in iTunes.  Here's a screenshot of upper left corner of my iTunes window, showing an iPod's device button (circled in red).  Click that button.

On the iPod's Summary settings screen, there is a sidebar along left side of window (below the tiny image and name of iPod).  In the sidebar, under Settings, click Music.  The iPod's Music settings screen is shown to the right.  If you are expecting iTunes to automatically sync music when you connect iPod, checkmark the box for Sync Music. 

NOTE:  Any songs currently on iPod that are not in your computer's iTunes library will be lost.

Then, set up that screen to tell iTunes how to automatically sync songs to iPod.  Click Apply to sync.  Going forward, iTunes automatically updates iPod (when you connect it or click Sync if already connected) with changes to iTunes music library, based on how you set up that screen.

If you want to manually load (and remove) songs on iPod, back on the iPod's Summary settings screen, checkmark the box for Manually manage music [and videos].  And Apply.

Please post back with any specific questions.

take off songs from the nano and put on songs that I have in my library

If you are trying to do this manually, go the iPod's Summary settings screen (as described in previous reply).  Is the checkbox for Manually manage music [and videos] currently enabled (checked)?

Do you want to load (and remove) songs manually, by dragging songs to the iPod in iTunes?

Or do you want to set it up so that the iTunes updates the iPod automatically (whenever you connect i), to keep it in sync with something like a playlist?

I would like to do it automatically but I would also like to make my on playlist and add that to my nano.

It's not a "but"...  You can set automatic syncing to sync a playlist (more than one if desired) to the nano.  Does your computer's current iTunes library have all of your songs?  Any songs on the iPod that are not in your iTunes library will be lost when you set up automatic syncing.

Also, based on what you said previously about not being able to do what I described, you may need to do a Restore in the iPod using iTunes (to give it a "fresh start").  This erases the iPod, reinstalls its software, and sets it to default settings. 

After the Restore, the default setting is to use the Manually manage music [and videos] setting.  That means it "syncs" but nothing gets loaded (because it's not yet set up to sync anything automatically).

Go back to my very first reply above (the one you marked as Solved).  Did you do what is described there to set up automatic syncing for music?

Funny that you marked that first post as Solved before your problem was "solved" (by mistake), and that's what finally actually solved your problem now.    Glad the old iPod's working again...