The overflow is running because the water level in the cistern is too high. Take the top off the cistern and you'll see the fill valve inside - often identified by a plastic ball that is fixed to a rod.. Flush the loo and you'll see the ball valve fall, allowing more water in. Can you see some sort of screw adjustment where the rod pushes into the valve as it rises? Unscrewing this, if you feel confident enough, will reduce the level in the cistern. Mind you, there are other types of fill valves which do look different....
John
April 2009