The author (or publisher) is responsible for obtaining copyright numbers for published work (not the editor). When you file for a copyright, the book is considered copyrighted from the date the paperwork is received in the Copyright office, even if the official documentation isn’t received by the author/publisher for several months. So make sure that you don’t submit your copyright paperwork until the book is final-final—right before it goes to print. It only takes a day or two. If you make changes to the book after you’ve received the copyright, you need a new copyright as the original copyright was for the previous version. Make sense?
My point? Make sure your work is absolutely final before you copyright it. This goes for digital books too, by-the-way.
Here is a website to access information and fees about all that: http://www.copyright.gov