|Turning on Home Sharing|
To do the Home Sharing method, just turn on Home Sharing on the old computer. Click File > Home Sharing. Enter your Apple ID.
Go to your new computer, click Store > Authorize this computer. Enter the Apple ID you used in your old computer.
|Authorizing a computer in iTunes|
Warning: This may take a while if you have an extensive collection and you're connected over slow wifi.
|Exporting Libraries and Playlists|
The good thing about this method is that it works, even if you've already put music into your new computer.