This is a common problem with water closets (commodes). It is caused by two common problems; you will find you have one or the other but the repair is fairly easy.
Either your 'flapper' is leaking by and allowing the tank valve to open and re-fill it, or your fill valve is set to make the water run into the overflow tube which would also make the valve kick in again to fill to the level that shuts off the valve.
You can pick up a new flapper at Wal-Mart, Lowe's, Home Depot or your local hardware store. Turn the valve down on the wall off to stop the flow to the commode, remove the flapper and take it with you to get the new one. There are a few different kinds and you need the one that works. Simply disconnect the chain that pulls the flapper open, remove the overflow hose at the top and slide the flapper up the overflow tube or slip it off the two spurs at the side. Re-insert the new flapper in reverse to the way you took it out and turn the water back on.
If it is the overflow tube that is draining the water out, you will need to adjust the valve to kick off at a lower level. For a ball cock valve, you may bend the arm to make the ball come higher or tighten a screw in the center of the tower to make it shut off at a lower level. For a tower float, there is a wire on the side of the tower and a butterfly depth adjustment on the float. Simply squeeze the butterfly togather and slide it up or down to get the level you need.
Let us know if you need further help.