This is a free HTML template for showcasing your YouTube playlist.
Here are the steps I followed to create this player:
1. I saved YouTube videos to my favorites.
2. I went to "My Account / Favorites" in YouTube and checked off the videos I wanted to include in THIS playlist.
3. I opened the menu at the top that says "Copy Videos To" and selected "New Playlist."
4. Then I was on a page called "Create/Edit Playlist," where I named the new playlist and gave it tags and so on. When I was finished, I clicked the Save button at the bottom of the page.
5. After that I was on the page for my new playlist, where I could edit it. At the top right is a button: "Create Custom Player." W00t! That's the ticket! Click that and get a player for your own playlist!
If you are signed in to YouTube, you can find a link at the top right of any page that says "My Account." Roll over it, and a menu opens, and you can select "Favorites" there.