You can't copy anything but pictures from your iPod to your computer, desktop mode is not supported with the iPod touch.
To copy the content from your Touch to your iTunes library on your computer, right click on it in the device list in iTunes and choose "transfer purchases". But you can only copy bought media and apps from the iTunes Store.
For all other songs you'll have to use 3rd party software like Touchcopy for example.
After that go to iTunes/Edit/Preferences/Advanced, to find out where the iTunes media are stored on your computer. This is the folder you need to back up somehow by moving the content to an external drive.