You need to transfer all the content of the old iPod to your computer and iTunes, and once it's in your iTunes library, transfer it to your new iPod.
For iTunes version 7 or later, then you can transfer purchased iTunes store music from the iPod to an authorized computer by using the "file/transfer purchases from iPod" menu. Note that the maximum of 5 authorized computers applies here.
Find out how to do that here.
How to copy iTunes purchases from an iPod to a computer.
For all other non purchased content (your own CDs etc) try this method which works on some Windows PCs.
Enable your iPod for disk use.
See:
iPod Disk Use.
Open iTunes and select edit/preferences/advanced/general. Put a check mark in the box marked "copy files to iTunes music folder when adding to library" and also "keep iTunes music folder organized", then click 'ok'.
Connect the iPod whilst holding down the shift/ctrl keys to prevent any auto sync, and if you see the dialogue window asking if you want to sync to this itunes library, click
'no'.
Then go to file/add folder, open 'my computer', select your iPod and click 'ok'.
The music files should transfer to your iTunes.
If this doesn't work (and it may not because officially it's not supposed to), check out the instructions/suggestions here.
Music from iPod to computer (using option 2). This a manual method using "hidden folders" and although it works, it is a little more involved than other methods.
Much easier ways are to use one of the many 3rd party programs that copy music from the iPod to the computer.
One of the most recommended is
Yamipod. This is a free program that transfers music from iPod back to the computer. However, it does not transfer playcounts/ratings etc.
Another free program is
Pod Player.
SharePod is also freeware.
If you want to recover just the structure of playlists from the iPod (and not the actual song files themselves), there's
iRepo for Windows. which I understand has this feature along with all the standard features for these programs.
iPodRip also has the feature enabling you to reconstruct playlists.
There is also
CopyTrans. This does preserve ratings/playcounts etc if those are important to you but this program is not free. It also supports video transfer.
