The inlet valve of your cistern should stop the water coming in before it reaches the overflow level - you need to adjust it.
Either lower the float further into the water or - more usually - screw in the little nylon adjusting screw and be sure to tighten its little locknut else it will soon start to overflow again.
Sometimes - not often - the rubber in the valve perishes and needs to be replaced. Mostly a two minute adjustment gets it fixed...
Operate the mechanism - pull up on the lever arm - see how the float arm shuts off the inlet water. All pretty basic.
Peccavi
January 2011