I am watching the video tutorial on Post Formats, but I do not appear to have the column in my post editor containing the different choices.
First, visit the Screen Options hanging tab at the top right of the page, to make sure that the Post Formats module is not simply disabled or hidden.
If you don’t see a Post Formats option in the Screen Options tab, then it’s likely your theme has not enabled support for Post Formats.
As we mentioned in the video tutorial on Post Formats, theme developers may choose to enable or disable support for Post Formats. It’s entirely possible that your theme doesn’t include support for specific Post Formats, or you may not see the Post Formats chooser at all.
If your theme does not support Post Formats, you’ll either want to find a different theme, or limit your posts to the default post format supported by your theme.
FWIW, Post Formats will change dramatically with the introduction of the all-new Gutenberg editor coming to WordPress 5.0, possibly eliminating the need for dedicated Post Formats altogether.
Stay tuned for more on Gutenberg, and I hope this helps!