A running toilet is a waste of money and that won't quit until you deal with the problem. The money that you spend in wasted energy is worth spending a few minutes to fix the problem and give you some peace and quiet. Here is a step by step list of some of the things you can do to fix the problem.
Adjust the Water Valve to the Correct the Water Line
When a toilet can't fill back up to the water the line it will continuously run. Take the tank off the back of the toilet and check to see where the water line ends once the toilet is finished filling. The water line is the dark line around the inside that the water to rise to in order to signal the valve to shut off and stop filling up. You can adjust the water valve to the lower setting by turning the screw to raise or lower the float.
Close the Flapper
In the event that you toilet flapper gets stuck in the open position, the toilet will keep running. If you see the flapper isn't closing you reach in the toilet and manually close it with your hands. Check to make sure that the chain is not interfering with the flapper from closing properly and if needed shorten or extend the chain to allow the flapper to close freely.
You can also replace the chain from the flapper with a piece dental floss that will work in the same fashion as a chain.
Replace the Flush Valve
Sometimes the toilet flush valve can get a mineral buildup over time and it will eventually malfunction. You can replace the flush valve by turning off the water and taking off the mounting bolts in the back of bowl. Remove the flush valve with a set of pliers. Install the new flush valve and put back on the mounting bolts. After tightening the bolts, turn the water back on to re-fill the bowl with water and let it fill up before testing it to see if it flushes properly.
If the above items do not fix the issue it could be a sign that you have a much larger problem and should call in a professional plumber. A professional resource like Hammond Plumbing will have experience in dealing with all types of toilets and the problems that cause that to malfunction.