Having a working knowledge of toilet plumbing is a handy thing indeed when dealing with home repairs. Fixing a constantly running toilet is a common issue that in most cases, takes just seconds to fix.
Just about everyone is familiar with the sound of a toilet that doesn't stop running. This issue is most commonly caused by one of two things: an old flapper valve that is no longer seated properly on the flush valve between the tank and the bowl or water leaking into the overflow pipe because of a float ball or pressure valve that is not floating properly. Both problems are easy to fix and do not require the help of a plumber.
To determine which problem you are having, lift the cover off of the toilet tank and have a peek inside. If your problem is water leaking into the overflow pipe, you'll know it because you will be able to see the water flowing in and, if you lift the float ball or pressure valve above the surface of the water, the flow will immediately shut off. A worn flapper valve that isn't seating may not be immediately obvious. In obvious cases, the water level in the toilet tank will not be high enough to push the floating ball or the pressure valve up high enough to shut off the flow of water or leak into the overflow pipe. If you can't tell by a quick look, try putting a couple of drops of food colouring into the tank and waiting a few minutes. If your problem is the flapper valve, the water in the bowl will start to turn colour before too long.
Repairs of this type take literal minutes. If water is seeping into your overflow pipe, simply bend the bar on the floater bar down a little bit so that the shutoff is kicked in a little sooner. With newer models, you'll have to tighten the screw at the top of the floating pressure valve, which will do the same thing; cutting off the flow of water earlier and preventing water from escaping into the overflow.
If your problem is the flapper not seating properly there are a couple of options available. The simplest is simply to jiggle the flush handle. Often times this will re-seat the flapper valve and negate any need for further repair. The next thing to look at is the link chain between the flush handle and the flapper mechanism. If it's kinked or snagged, it won't allow the flapper to actually seat at all. After a few seconds spent untangling it your problem will be fixed. If neither of these things fixes the problem, any issues can generally be solved by replacing the flapper mechanism. Toilet plumbing, for most toilets, cost just a few dollars, and the package comes with installation instructions.