Well, assuming they are dairy goats, it's one of the few things about ADGA that is straightforward. It you breed your boy to a registered girl, they have an online form, you select a registered name for their offspring, fill out the sire, dam, birthdate, and some token appearance information and pay a small fee and you receive their certificate. If you register a herd name in advance ($15/year or $100 permanently, I believe), your herd name will appear as the beginning of each animal's registered name.
In my opinion registered goats are totally worth it because you can see the detailed lineage information, know your inbreeding percentages, and keep track of your lines in a more effective way than if you have unregistered animals. I have both registered and unregistered on my place, and my unregistered gals are still beloved, but if I could go back in time I would do all registered just because it appeals to the detail-oriented part of me!