Here is an example of a video embedded in a standard format posting:
All that was required was to include the URL to a YouTube video on a separate line in the text of this post. The WordPress documentation about posting formats lists “Video” as one of the possible choices, but that choice was not presented to me in the Add New Post or Edit Post screens. (I’m not sure if the documentation is outdated in this regard.) Since WordPress’ auto-embed mechanism (enabled by default) seems to do a nice job within the Standard posting format, I didn’t need to specify the mysterious Video format. See the Settings, Media screen for WordPress options relating to Embeds.