A closet auger is a drain clearing tool designed specifically for use with a toilet. It is designed to clear the toilet through to the drain pipe under or behind the toilet. For blockages further along in the drain line, waste stack or sewer pipe, a closet auger will not be effective. A closet auger has a reach of roughly 3 feet; some models are slightly shorter or longer.
If after using a plunger, the water is not draining out of the bowl as it should, you can use a closet auger. Typically it has a sharp spiral of wire on the tip and a semi-rigid wire that can flex through the bends in the toilet bowl. It also has a guide tube and an offset hand crank, to turn the spiral tip and clear the obstruction. Do not use other types of drain snakes with a toilet as they can damage the toilet.
Retract the cable through the handle so the tip of the cable is at the end of the guide tip.
Insert the guide tip with the curve facing the direction of the drain. Some bowls drain to the front and some drain to the rear, which can be seen simply by looking into the bowl.
Crank the auger in one direction until is becomes tight then crank in the other direction. Repeat this until the auger is in as far as it will go.
Crank the auger to clear the obstruction.
Pull the guide tube out of the toilet. If it gets stuck push and pull gently or turn a crank back and forth while gently pulling up. Do not force the auger or you may break the toilet bowl.
After breaking up the clog, use the plunger to move the material down the drain line.
If the water seems to be properly draining, go ahead and try flushing the toilet.