How Do I Copyright Children's Book?

Dear Rich: We have a wonderful book about ready to send to the printer. The idea for the story came from my wife and I. We contracted with someone to write and illustrate the book. We have had many discussions along the way where we changed text and the order of the story, even getting together for a couple intense days of rewrite. We have this section in our contract: 

A. The Author hereby grants and assigns to the Publisher, its successors, representatives, and assigns, the sole and exclusive right to publish (i.e., print, publish, and sell) the Work in the English language in all forms in the United States of America, its territories and dependencies, and Canada, during the full term of copyright and any renewals and extensions thereof, except as provided herein. 

My question is how do we actually copyright the book? Does the author have to do it and the contract gives us control or can we copyright it ourselves?

Under your contract provision, the author retains copyright to his or her contributions and grants to you, the publisher, the exclusive North American English-language book publishing rights. The author retains all other rights (unless the contract states otherwise) including foreign, translation, book club, film and television, audio, and dramatic rights.
Co-authorship? Your contributions -- story ideas, structure, rewrite -- may make you co-authors of the text, and possibly of the illustrations as well. In that case, the book would be considered a joint work, and you, your spouse, and the author would all be co-owners of the copyright.
Registration. Although registration is not mandatory, it is strongly recommended. Anyone who owns all or part of the rights that make up a work’s copyright may register that work. Therefore, because you retain those exclusive North American publishing rights, you can file as copyright owner of those specific rights. You would name the author (person who did the text and illustrations) as author, and if you determined that you and your spouse were co-authors, you would add your names as authors as well. By the way, you should be able to register the text and illustrations on one application (as a "single unit").