After installing iTunes on the new computer, go to the old computer and find the folder iTunes in the My Documents\My Music folder. Copy that entire folder to the same place on the new PC. Reboot and open iTunes.
I have a laptop that I use for about everything, but I never kept my iTunes library on it because it would take up too much space, so I just kept it on my desktop. I saw the how to video on moving the files to an external hard drive, and that would be perfect in my situation since I can have it on my laptop without using the internal hard drive's space. The video didn't say anything about backing up and swithing to a new computer, though, so would I have to go through any extra configuration options to do that?