Watch this video from This Old House to learn how to fix a running toilet.
1 Turn off the water at toilet's shut-off valve.
2 Remove the rubber flapper from flush valve inside the tank.
3 Inspect flapper for damage or discoloration.
4 Check location of float on chain; adjust float to height of water level.
5 If adjusting float doesn't solve problem, or if there is no float, install a new flapper.
6 Flush toilet and check to ensure new flapper creates watertight seal with flush valve.