If your toilet tank won't stop filling when you flush it, then it is wasting your water and money, as well as generating an annoying noise. There are a number of different issues that could be causing this problem. However, there is probably no need for the expense and hassle of calling a professional plumber, since you should be able to easily clear up these issues yourself.
The first thing to check is the flush lever. It is also the easiest problem to fix. Remove the lid of the tank and locate the flush lever. This is the metal rod that is connected to the toilet's handle. When the handle is pressed, the lever moves up. This pulls up the flapper valve on the bottom of the tank by means of a chain. Try tightening it by hand to see if it has come loose from the handle. This nut is usually threaded in the opposite direction from most nuts, so turn it counterclockwise to tighten it.
Once you've checked the flush lever, check the chain that connects it to the flapper valve. If the chain is so tight that the flapper can't set itself on its rim, then remove it from the flush lever and reset it with a little more slack. Ideally, the chain should have about ½ inch of slack in it.
Water Level Setting
If you've determined that it isn't the flush lever or chain, then the problem may be that your water level is set too high. This causes the water to spill into the overflow tube, which is the large upright rigid tube in the tank. Because the water is draining into the overflow tube, it never rises high enough to trigger the intake valve into the "Off" position. To determine if this is the culprit, look to see if the water in the tank is at the top of the overflow tube. If it is, turn the screw on the top of the intake valve, which sits on top of the overflow tube, to lower the water setting. If yours does not have a screw, then your tank has an adjustment knob at the bottom, near the flapper valve. Once you've adjusted the water level, flush the toilet and see if the water stays below the top of the overflow tube.
If water level isn't the cause of the problem, either, then take a look at the flapper valve. To do this, first turn off the water line to your toilet. The shut-off valve is usually located directly behind the toilet, on or near the wall. Flush the toilet to drain the water out of the tank. Look at the flapper valve. If it is chipped, rough, uneven or misshapen, then it is damaged and not sealing properly. Alternatively, pour food colouring into the tank while it is full. If the colouring appears in the bowl without flushing, then the flapper valve is leaky.
If none of these attempts work, then remove the top from the fill valve if it has a removable cap. Remove the loose washers and other parts and inspect their seals to see if they need replacing. Also check for dirt or debris that may be clogging the fill valve and preventing it from working properly.