How do I troubleshoot the following?

The plugin is enabled but all that displays is the tag i.e. {youtube}youtubeID{/youtube}

The video player does not show

I have the same issues.
Joomla! 3.4.5 and AllVideos 4.7

AllVideos is a content plugin. You need to place the tag in a context where content plugins are supported ( an article, a K2 item or a module for example ) .

So clarify where exactly are you using that code so we can help you both.

Same problem. No matter whether I put it into an Article or into a Module... only shows the tags. Latest Joomla version and latest AllVideos. How come and what can I do to solve it?

@Brigitta Deistler

Which module are you using? If you are using a Custom HTML module remember to set the option "Prepare content" to "Yes".