Once you have all of the components created, you'll just want to put them in a folder to zip up, and then rename using a .epub file extension. From here you'll likely want to test the epub, which you can do using calibre or any other ebook reading program.
One helpful tip is to use a epub checker, such as this free one online http://validator.idpf.org/. Keep in mind the errors are frequently only indirectly related to the problem, so if it's telling you you're missing a file that you know is there, you may want to check the file structure for duplicates or typo's.
Additionally this book you've been watching being written is available to view here on github, including the proper file structures and such https://github.com/thansen0/sample-epub-minimal. Keep in mind it may be slightly different, as I may be updating them at different times.