Press the anchor button on the bottom left of your screen, then click on the top bollard icon, and press the yellow circles on the ship that hold the lines you wish to let go of.
And after the new patch (v1.1 -> v1.2) those Yellow Mooring Balls will change to red when you are moored. Visible in the Demo Version.Same for the Green Towing Balls. They also will change to red.See Attachements