The Mac Developer Program ($99 per year) will let us to create Developer ID certificates that we can use to codesign our apps and prevent users from seeing scary warnings when they try to launch our stuff.

MetaBrainz first needs to be assigned a D-U-N-S Number (http://www.dnb.com/get-a-duns-number.html), which are said to be free. You can apparently get one through that link.

You then have to create a personal Apple ID, if you don't already have one, before you can enroll an organization in the developer program. Start here https://developer.apple.com/programs/start/standard/create.php

Once you create an Apple ID it should guide you through the enrollment. From what I understand you just need a DUNS number, business address, and credit card.

After you've enrolled you can apparently add developers to the organization's team, who can presumably do all the dirty work of creating certificates and signing apps.