Problem 1: Water Trickling Into the Bowl, or "Phantom Flushes"
You may periodically hear your toilet begin to spontaneously refill, as though someone had flushed it. A toilet that cuts on and off by itself, or runs intermittently, has a problem that plumbers call a phantom flush. The cause is a very slow leak from the tank into the bowl. This problem is almost certainly caused by a bad flapper or flapper seat. The solution is to drain the tank and bowl, check and clean the flapper seat, and replace the flapper if it's worn or damaged.
Problem 2: Water Trickling Into the Tank
If you hear a sustained hissing sound coming from your toilet, it's probably a result of water trickling into the tank via the supply line. In this case the parts to check are the float, the refill tube and the ballcock or inlet-valve assembly. The hissing sound is typically caused by water coming through the inlet valve. First check to see whether the float is sticking or needs adjusting. Next, check to make sure the refill tube isn't inserted too far into the overflow tube. (It should extend only about 1/4" below the rim of the overflow tube.) If neither of these adjustments solves the problem, you'll probably need to replace the ballcock assembly as described above.
Problem 3: The Bowl Empties Slowly
A bowl that empties slowly -- also known as a weak flush -- is usually the result of clogged holes underneath the rim of the bowl. Use a curved piece of wire to poke gently into each flush hole to clear out any debris. Coat-hanger wire works fine, and a small mirror will help you see under the rim. You can also use wire to loosen debris that may be blocking the siphon jet in the bottom of the drain. Be careful not to scratch the bowl.
Problem 4: The Dreaded Clog
Clogs are the most common toilet problems. Several tools can help you clear a clogged drain. A force-cup plunger is more effective than the familiar standard type for clearing minor clogs. Insert the bulb into the drain, and pump forcefully. Slowly release the handle, letting a little water in so you can see whether the drain is clear. Repeat if necessary.
For serious clogs, use a closet auger. Insert the end of the auger into the drain hole, and twist the handle as you push the rotor downward. Use caution not to scratch the bowl.