Thanks for reaching out to us about this!
Since you're on the free version of Spotify, your personal playlists will automatically be shuffled. This is indicated by a blue icon with white 'shuffle' arrows next to the title of the playlist. In order to be able to listen to your playlists on demand, you will have to upgrade to Premium.
There is, however, a selection of playlists which are available on demand if you're on free. These include the Made for You playlists, including Discover Weekly and Release Radar, as well as some popular Spotify-curated playlists. You can check which ones by clicking on the Home tab and scrolling down it - the ones without the blue shuffle icon are available on demand.
Hope that clears things up! Let us know if you have any further questions about this.