Itunes is an on-line store and an application. Download the application as snags described.
BUT your Touch will not sync it's tunes back to iTunes, it is a one way sync from iTunes out to the ipod.
If you have all your music on the Touch you can get programmes that will sync back to iTunes. Search on here there have been plenty of answers with suggestions. If you have more music on your old system than on your Touch then you need to move your iTunes folder (including the iTunes Library and iTunes artwork) onto your new system, replacing the empty iTunes folder that would have been set up when you downloaded the iTunes application