Probably the most straightforward way to get iTunes onto your second computer is to network it with the first one and copy your iTunes folder across. Start by consolidating your library. When you consolidate, any songs in the iTunes Library that are not in the iTunes Music Folder are copied to the Music Folder and the Library is updated to point to those new files. Files already in the iTunes Music Folder have no changes made to them:
Copying all your iTunes files to one location - Windows
Copying the whole folder brings with it the iTunes Music folder and also the iTunes Library (iTunes Library.itl in Windows) database file which holds all the information about your songs (Playlists, Ratings, Play Counts, Last Played, Date Added, etc). You'll get more information including the Folder/File structure in this article:
What are the iTunes library files?
When you copy the iTunes folder make sure you put it into the same location on the new computer. This has to be the exact same place, on a PC this is \Documents and Settings\Username\My Documents\My Music\ (or C:\Username\Music\ in Vista). Everything has to be exactly the same on the new computer including the Windows user account name. When you open iTunes on the new computer it will be the same as on the original one Songs, Playlists, Play Counts, Ratings etc. You should also use the same version of iTunes on both computers.
You can also use this method with an external hard drive, you drag the folder from the first computer to the external drive and then from the drive to the second computer.
If you have an iPod it can be used as an external drive and you can move the iTunes folder onto it:
How to use your iPod to move your music to a new computer
If you have any iTunes purchases in your library don't forget that you'll need to authorise your new computer to play them. Also if you are disposing of the old one remember to deauthorise it so you don't use up one of your allowances:
About iTunes Music Store Authorisation and Deauthorisation
