You do need to physically move the music files from the old computer to the new computer.
First of all though "authorise" the new computer, this will enable it to play any content that is protected. If you don't have an iTunes account and have never bought anything from the store skip this bit. Go to iTunes on the new machine, then from the "store" menu select "authorise computer" and finally enter in your iTunes account details.
Now you need to move the music, for this you'll need an external disk drive or to be able to view files on your old computer from your new computer. Basically find where the music files are on your computer and copy them. If you need help with this then let me know what type of computer you've got and I should be able to help you out.
Then on the new computer drag all of those files into iTunes.
Finally if you had an iTunes account deauthorise the old computer. From the "Store" menu select "deauthorise computer".
And that should be that.
Albeit with a potentially very big hole in the middle of how to actually move files from one machine to the other...
I've sorted it. I found some fab free software last night called "pod to pc" and it did it for me. Took ages though as the free version will only do 10 songs and then makes you wait a minute before doing the next 10. Was very simple though.