Moving a library: Quick answer if you use iTunes' default preferences settings: Copy the entire iTunes folder (and in doing so all its sub-folders and files) intact to the other drive, hold down the option/alt key (shift on Windows) while starting iTunes, and when requested to select a library select the iTunes Library.itl file in the copied folder. https://support.apple.com/HT201596
Remember to authorize the computer in iTunes to your Apple ID if you use this to sync to Apple mobile devices or play DRM protected media (e.g., movies).
Certain items used in iTunes related activities are not stored in the iTunes library folder but in special folders. If you are moving a library to a different computer you may wish to copy these too:
- Apple Music cache files: http://dougscripts.com/itunes/2015/09/new-flush-apple-music-cache-files/ - ~/Library/Caches/com.apple.iTunes/SubscriptionPlayCache/ folder, which is sort of like an “iTunes Media” folder for Apple Music
- iOS device backups, various preferences files: https://discussions.apple.com/thread/3285925
Windows users see tip at: https://discussions.apple.com/message/18879381#18879381