Your ballcock will need adjusting so that the water input is cutoff when the ball is lower. Usually a simple nut and locknut. Slacken the locknut, turn the adjusting nut to the required position, then retighten the locknut. Use a spanner but do not use too much force, they can break easily.
However, if part of it has broken already I'd buy a complete new style Quiet Float Valve without the arm and ball. Fluidmaster make a good one available from Homebase etc. Make sure you get the right type, either bottom inlet fitting or side inlet fitting. You'll need to turn off the water supply to the cistern before you change the valve.
ChicksFan
August 2008