Disclaimer

I am not a lawyer. Go hire one if you need legal advice. Also, I am located in the United States, and this answer is given in that context. Things may be a little (or a lot) different if you're in a different country.

Transferring Copyright

It's like anything else in business: you and your client sign a contract in which you agree to assign your copyright to the client. You could use a stock version like the one I linked above, or have your lawyer come up with something specific to your business, maybe an optional addendum to your standard contract. If you want to transfer the copyright on multiple photos at once, you'd naturally specify all of the photos in the agreement.

Registration

Copyright and copyright registration are two different things. When you create something like a photograph, you as the creator own the copyright. If you think it's an important enough work that people might argue about who owns it, you can register your copyright with the US Copyright Office. If you transfer your registered copyright, you'll want to record the transfer with the Copyright Office. The Copyright Office explains in some detail how to do this, but the short and sweet version is that you send them a certification of the transfer (and a fee, naturally), and then they record it and send back a certification that the transfer was recorded.