When my wife got a new computer, and then when I did. We each have our own iTunes libraries.
It is kind of complex, and it seems every search result you find on the Internet recommends a slightly different way to do it.
The EASIEST way is probably to download this product and pay $15.
http://www.ipodsoft.com/site/pmwiki.php?n=igadget.HomepageThe harder, but free, way that I used involved copying the iTunes Music Library folder plus its XML index file to the new computer, then doing a global search & replace on that index file to change the path name for EVERY song in the library - you need to do this if on the new computer, the iTunes folder is in a different location. (Likely unless they are running the same OS, and were set up the same way with the same username for you.) Let me know if you want more info on this procedure.