Moving iTunes Library
Moving between computers is easy. Just copy the entire iTunes folder found in your ~/Music folder. You should sign off from the iTunes Store and de-authorize the old computer first.
But what if you want to move your music to a new location on the same computer such as a larger hard drive? The safest way is to leave the iTunes folder and everything inside where it is. Inside iTunes and choose Preferences from the iTunes menu. On the Advanced tab, set the new location where you want the library to reside. Then go to the File menu and choose Library>Organize Library… In the resulting dialog window, select Consolidate Files. This will copy the music to the new location. After you have verified that iTunes is working correctly, you can then delete the original music folder which is at ~/Music/iTunes/iTunes Music.
Best practices dictate that you have a good backup of your iTunes folder before attempting this.