1) install itunes on new computer.
2) Copy "itunes" Music" folder from old computer to external HD. Everything WILL be in this folder if this option in preferences is checked:
3) Replace the iTunes Music folder on your new computer with the iTunes Music Folder from your old computer. These are the locations:
- OSX: /Mac/Users/UserName/Music/iTunes
- XP: C:\Documents and Settings\Users\UserName\Music\iTunes
- Vista/Win7: C:\Users\UserName\Music\iTunes
4) Go to Store->Authorize Computer, and sign-in to your itunes account.
5) Go back to itunes, and go to File->Add Folder to Library, select your itunes music folder, and let itunes analyze everything. When that process finishes, you should be good to go.