To start a new group as an existing user you will need to navigate to the profile icon at the bottom right of your screen.

You will see your existing WordGo group(s) along the top of the screen, and to begin a new group you will click the un-coloured, dotted circle with 'start a new course' inside it.  

If this is not immediately visible, it may be that you already have multiple groups and you simply need to swipe left in your groups area to see this icon.  It will be at the far right end of your group circles.