Replace the flapper first. A worn flapper is the most common problem, and it can make a toilet flush on its own. Before you replace anything, do the dye test below to confirm the tank is leaking into the bowl.
The dye test
Put a few drops of food coloring in the tank and don’t flush. If color shows up in the bowl after 10 minutes, water is leaking past the flapper. Flush afterwards so the dye doesn’t stain. A pencil mark at the tank water level works too, with a longer wait: 10–15 minutes for Fluidmaster, at least 25 for Korky.
Before you change the flapper or fill valve, turn off the toilet’s shutoff valve (the small valve on the wall behind it) and flush to empty the tank.
Check these in order
The flapper is worn
How to tell: The dye test shows color in the bowl, or the toilet refills by itself every so often. A fill valve that turns on and off by itself means the tank is losing water.
Fix: Clean the flapper and the seat it sits on; if it still leaks, replace the flapper. Bring the old one or a photo and check whether you need a 2" or 3": see toilet flapper size. Replace flappers at least every five years.
The chain is too short or too long
How to tell: The flapper is held slightly open, or the chain gets caught under it.
Fix: Leave a little slack: about 1/2" for Fluidmaster, 1 to 2 links for Korky. That way loose chain can’t fall under the flapper and a tight one can’t hold it open.
Water is running into the overflow tube
How to tell: Take the lid off: the water level reaches the top of the open tube in the middle and spills into it.
Fix: Lower the water level to 1/2" below the top of the overflow pipe. If it won’t stay down, clean the fill valve; if that doesn’t fix it, replace the fill valve.
The flush valve is damaged
How to tell: The water level drops to a point on the overflow tube, or to the bottom of the tank, even with a new flapper.
Fix: Clean any mineral deposits from the drain opening; if it still drops, replace the flush valve.