You may refer to this guide, it's regarding how to transfer iTunes library to another computer
It works pretty well for me.
I purchased an audiobook on my office computer, but I use my home computer to sync with my iPhone. Now I can't download the book to my home computer without having to pay again AND I can't sync with the office computer without erasing all of the info and apps from my home computer. ITunes considers my home computer as the master library. I didn't know all of this and, quite frankly, don't understand why it has to be this way. Can anyone suggest a solution?