Pressing down on a toilet handle to be greeted only by silence is an empty feeling. If you've checked the bowl and you're sure that the toilet isn't clogged, yet it is still having a problem flushing, you'll need to take a look at some of the hardware inside the tank. Once you've identified the problem, the solution is quite easy to implement.
When you press down the handle on a toilet, it begins a number of processes. The handle lifts up a rod inside the tank. Connected to the rod is a chain. The chain, in turn, lifts up the flapper in the bottom of the tank. Once the flapper is open, the water inside rushes out into the bowl. The float inside the tank lowers as the tank empties, which triggers the fill valve to refill the toilet tank so it is ready for another cycle.
One reason why a toilet might not be flushing is because of a broken or disconnected chain. Remove the toilet tank lid and set it aside. You should see a chain running from the toilet tank handle rod down to connect with the flapper. If it's not, the chain should be reconnected at either the handle rod or the flapper. Check that the toilet chain isn't tangled up, which can also cause the toilet not to flush.
A tank that isn't filling properly won't flush. One reason for a non-flushing tank could be a stuck float. There are two major types of floats: a ball float and an integrated float. Ball floats are found on older-style toilets. These are connected by a long rod to the fill valve. An integrated float fits around the fill valve in a donut-type shape. In either case, gently grasp the float and raise it up and down several times to see if it can be unstuck.
Bad Fill Valve
The problem in a toilet that doesn't flush could also be the fill valve. The fill valve is connected at one end to the water supply for the house. Water rushes into the fill valve and out into the toilet tank. Most modern fill valves have antisiphon valves incorporated into them to prevent water from flowing out of the tank and into the municipal water supply. The easiest way to fix a bad fill valve is simply to replace it, as these parts aren't expensive, and you might be breaking local plumbing codes if you attempt to repair an antisiphon fill valve.