how can i fix my toilet cistern?

it sounds like its overflowing - if so you will have water flowing from your overflow pipe. That L - shaped bit as you say should have a ballcock connected to it ( a bar with a ball or float on the end ).
Lift this up with your hand ( does the water stop flowing). there is an adjustment screw that adjusts the height as to which the water stops flowing also check the bar is not bent. If when lifting it up by hand the water dont stop flowing then you will need to replace the valve.

Gary
January 2006