Hi,
You need to adjust the ball cock (no childish giggles please!!)...
Take the top off your cistern and you should find a lever with a plastic hollow ball near the end.
You should be able to adjust the hight that the plastic ball sits in the water by either slding it along the lever, or screwing it up or down. This in turn should lift the lever which switches the valve at the other end of the lever to the ball to the off position.
If water still dribbles through, you have a leaking valve, which can be replaced, but you will have to turn the stop cock off under you sink to do so!!
Good luck..
Lest
October 2008