Some people get confused because they see the LW playlist within iTunes & think the songs are already within iTunes Music Library. But this isn't the case. That's only a playlist & the songs will still exist within your LW downld folder. They must be added using techniques as suggested by rkapsi or a couple of xtra techniques suggested in the thread I refered to in my above post.
* Go to iTunes preferences >Advanced & make sure the option
'Copy files to iTunes Music folder when adding to library' is ticked. (see image below: win to left & mac to the right.)
You should also make sure you have the most up to date iTunes & iPod softw. Update both.
iPod Tutorial:
http://www.apple.com/support/ipod/tutorial/index.html
Remember you can add songs manually & this is probably the wisest way to add songs to your iPod.
As Only A Hobo hinted, if you're using mac osx then it's much easier to set up as iTunes can be made to automatically import the songs to its music library. But this only applies to mac osx.