To embed a playlist into a blog or website open the Share menu associated with a playlist then copy the embed code provided.
If you are playing a video within a playlist on YouTube you can find the embed code for the playlist below the video that you are currently watching.
My playlist of Practical Ed Tech tips is embedded below.
An additional method for getting students to watch the playlists that you create for them is to ask them to subscribe to your YouTube channel. This option is only available if your students have YouTube accounts of their own.