File Migration -- Tiger HD to Lion Mac mini

I have a new Mac Mini running Lion 7.2. I also have the HD from my old iMac which ran Tiger 10.4.8. The HD from the Tiger machine is in an eSATA HD case connected to the Lion mini through USB. I can see the files on the Tiger HD. How do I migrate the files to the Lion mini -- I'm particularly interested in my iTunes library. Is it as simple as just copying the files and pasting them into the Lion's iTunes folder? If there's more to it, then please provide step-by-step instructions.

Thanks to all who reply.

You will be using file migration app
can be found in finder /Applications/Utilities/
or you can go here http://support.apple.com/kb/HT4413?viewlocale=en_US&locale=en_US

OK -- I connected the old Tiger HD and turned it on. The Mac HD icon with the USB symbol shows up on the desktop. I open Migration Assistant, log in, and select transfer files from a Time Machine Backup or other disk. I click continue and on the next page I get the spinner and a message saying it is looking for another computer. The Tiger HD is not showing up in MI. After a couple of attempts, I quit and ejected the Tiger disk. I am able to view all my files on the Tiger HD in the previous system folder. It's all there. Why doesn't MI find it?