How to use the youtube module? I've added and enabled the YouTube module and I'd like to put a YouTube video on my page but I can't figure out how.  

I think there is a youtube widget somewhere but I can't find it or get it onto my site.
I assume you mean this module? https://www.drupal.org/project/youtube

If so this module provides a field for your content type of choice where you need to display the video. The most basic content type to start with is "Basic Page".

Once you add this field, when you "add content" for this youtube field you can specify it's URL. When you view this node/entity the video player should show up. This module does have the ability to render the Youtube player, but there's a chance you may have to configure your content type view mode.

This Youtube video has more details on the setup for the Youtube Field module - Youtube Field Setup Video