Spotify has created a widget for music lovers to simply embed playlists, songs or albums to a website. For this to work you and your readers will need to have a Spotify account (free one will work) and have the Spotify app installed.
To get the widget, first visit this web page: Spotify Play Button, then launch the Spotify application. In Spotify right click on any song, album, or playlist you'd like to share. Click "Copy Spotify URI". Take that and paste it into the form on the web page to generate the embed code. Finally copy the embed code and use it on your website.
If you would like to listen to more of my shared playlists, just look for programwitch on Spotify.
Enjoy.