There's a valve to control the water. Take the lid off the cistern and flush it a couple of times and watch the action. See the float drop down and rise up. See how the inlet valve is operated to close off the water. Pull up on the moving arm to make the valve close.
You may need to change a washer in the inlet valve but more often a simple adjustment will fix it. Either lower the float to make the valve shut off sooner or screw in the little nylon adjuster to do the same thing - tighten the locking nut else you'll be re-adjusting it every week.
Peccavi
August 2009