Music is intended to go one way: from your computer to the iPod. Going the other way is contrary to the design and is not trivial.
See this old post: https://discussions.apple.com/thread/2452022
Since it is so dated some of the links may not work.
iTunes will only give you the option to copy your iTunes Store purchases directly from an iPod to the computer, you'll find details in this article: Copying iTunes Store purchases from your iPod or iPhone to a computer
For everything else (music from CDs, other downloads etc) there are a number of third party utilities that you can use to retrieve the music files and playlists from your iPod. You'll find that they have varying degrees of functionality and some will transfer movies, videos, photos, podcasts and games as well. You can read reviews and comparisons of some of them here:
iTunes & iPod software
Wired News - Rescue Your Stranded Tunes
Comparison of iPod managers
A selection of iPod to iTunes utilities:
TuneJack Windows Only (iPhone and iPod Touch compatible)
SharePod Windows Only (iPhone and iPod Touch compatible)
iPod2PC Windows Only
iDump Windows Only
YamiPod Mac and Windows
iPod Music Liberator Mac & Windows
Floola Mac & Windows
iPodRip Mac & Windows (iPhone and iPod Touch compatible)
iPod Music Liberator Mac & Windows (iPhone and iPod Touch compatible)
Music Rescue Mac & Windows (iPhone and iPod Touch compatible)
iGadget Mac & Windows (iPhone and iPod Touch compatible)
iRepo Mac & Windows (iPhone and iPod Touch compatible)
iPod Access Mac & Windows (iPhone and iPod Touch compatible)
TouchCopy Mac & Windows (iPhone and iPod Touch compatible)
There's also a manual method of copying songs from your iPod to a Mac or PC. The procedure is a bit involved and won't recover playlists but if you're interested it's available on page 2 at this link: Copying Content from your iPod to your Computer - The Definitive GuideHow to use your iPod to move your music to a new computer (does not apply to the iPod Touch)
Well first, you need to switch your iPod to manual sync. Then you can plug it in. It will ask you if you would like to put new songs on your ipod into iTunes library again. well it should anyway. well, if it doesn't then switch your sync options to manual. hook up your iPod, then click and drag the music tab underneath you iPod into the library tab,
That works for me.
Open iTunes on the pc. Plug ipod in. Click on your device in the column on the left. Check 'back up to this computer'. Enjoy.
Next click on icloud and sync you backups there.
Lastly, you can always transfer your songs to a cloud service like iPod to PC transfer, assuming you have less than 5gb of songs. Then you can access your songs anywhere, on any device, at any time.
Step1: Download the Pod to PC transfer.
Step2: Change your sync mode to Manually-Sync before connect to your iTunes.
Step3: Run iPhone to PC transfer and transfer all your music you want to add to iTunes to your computer first. This tool will not erase anything on your iPhone or iTunes.
Step4: Add music from your computer to iTunes.
That nice software works with Windows only and costs a bit more than 20€, but the OP didn't state any OS preference anyway.