The incessant drone of water running in your toilet has two common causes, and each can be easily solved the appropriate method.
This happens when water leaks through the hole at the bottom center of the tank under the flapper because the flapper does not seat properly. There are two possible culprits for this: the flapper chain or the flapper itself. The flapper chain connects the flush handle arm to the flapper. Sometimes the chain gets twisted, snagged, or caught on the handle arm, which shortens the chain’s length, holding up the flapper so it can't seat fully.
The ideal chain length has some slack when the handle arm is at rest and the flapper is fully seated. Make sure the flapper chain is untangled. Flush the toilet a few times to assure the chain does not re-tangle and the flapper seats properly. I have seen corroded handle arms, rusted chains, and broken links. I've used string, a twist tie, and a paper clip to temporarily repair flapper chains. Later, replace the old chain with a new one.
Considering the flapper itself, I have encountered all of the following: flappers so old some of its rubber has been eaten away by water; the rubber loop the chain hooks into has disintegrated; and one or both of the hinges have eroded or merely slipped off its posts.
Follow these instructions to repair or replace the flapper:
Step 1 - Test the Flapper
With tank lid off, handle at rest, and toilet seat up, push down the flapper. If the water stops running into the bowl, the flapper needs to be repaired or replaced.
Step 2 - Test the Chain and Hinges
Make sure the chain end is fastened securely to the flapper loop, so the flush handle operates the flapper correctly. Make sure the flapper hinges are attached securely onto their posts (bottom of overflow tube), so the flapper floats up and down freely.
If the flapper still does not seat correctly, then install a new flapper.
Step 3 - Shut off the Water
Turn the shut-off valve (below the tank) clockwise to shut off the tank’s water supply. Remove tank water by flushing the toilet.
Step 4 - Remove the Old Flapper
Disconnect the chain from the top of the flapper. Disconnect the flapper’s hinges from their posts. Remove the old flapper.
Step 5 - Install the New Flapper
Attach the chain to the new flapper, then set the flapper in place, attaching it to the hinge. Connect the chain to the flush handle arm. Now you can turn the water back on.
Running Overflow Tube
Sometimes, tank water is flowing over the top of the overflow tube in the middle of the tank. Check the tank water level; optimal level is a 1/2-inch below the top of the overflow tube. If water flows into the top of the overflow tube, then the float assembly’s adjustable float is not working properly. Readjust the float by increasing the length of the rod connecting the float to its arm. If float adjustment does not stop the water level at a 1/2-inch below the overflow tube top, then replace the old float assembly with a new one, following these instructions:
Step 1 - Turn the Water Off
Turn the shut-off valve (below the tank) clockwise to shut off the tank’s water supply. Remove tank water by flushing the toilet, scooping out leftover water, and drying with rags.
Step 2 - Remove the Old Float Assembly
Loosen and remove the nut at the bottom of the float assembly at underside of the tank. Unclip the float arm from the overflow tube and remove the old float assembly.
Step 3 - Install the New Float Assembly
To install a new float assembly, reverse the above steps. Clip the float arm to the overflow tube and secure the the nut at the bottom of the float assembly at underside of the tank. That done, turn the water back on and adjust the float to the proper depth.