A clogged toilet is very common. When someone asks about this, I usually ask if they have small kids. I don't know what the fascination is, but kids love to throw stuff in the toilet and watch it swirl down the bowl. They only stop after they have been caught, but by then any item that can fit into the toilet has been flushed, and the damage has been done.
A toilet is a unique plumbing fixture because the trap is built into the toilet and not into the drain pipe (if you look under your sink, you will see the trap in the drain pipe). The water in the bowl seals out the sewer gasses from entering the room, as well as provides a medium for the waste.
I have never used chemicals to clear a toilet. They take too long to work and typically are made to work on hair and grease. You have a couple of different choices. You can use a plunger, a closet auger or hydrostatic pressure.
Hydrostatic pressure is a fancy way of saying that you are going to force water down the bowl. This works fairly well if the water level in the bowl is low. Simply take a bucket (a five-gallon bucket is good), and fill it about half full. Hold it waist high and pour it into the opening at the base of the toilet bowl. The pressure of the water entering the trap from a height may solve the problem. If the water level in the bowl is normal or even high, go right to the plunger.
My tool of choice is the plunger. Use a toilet plunger that seals well against the toilet (don't use a plunger that looks like a cereal bowl turned upside down).
The best plungers can move a large volume of water quickly. These are bell-shaped with a narrow opening on the bottom. The trick with a toilet plunger is to get rid of the air in the plunger and replace it with water. Air will compress but water will not.
Place the plunger into the bowl and under the water at an angle and gently compress it to expel the air. When the plunger expands again, it will fill with water. Now stick it into the opening and with a quick motion, jam the water in the plunger down the hole. Keep the plunger sealed against the opening and gently let it refill with water, then jam it down again.
There are different methods of plunging. Some people move the plunger in and out quickly, but I have found more success in dislodging the obstruction with this method. Try a couple of test flushes to see if you can call it quits. If it still backs up, move to the closet auger.
A closet auger (aka toilet snake) is a short plumbing snake with a rubber boot on it to prevent scratching the porcelain. It has a corkscrew-shaped end that grabs the obstruction or sometimes pushes it through.
Have a bucket or bag nearby to place the wet snake (or plunger) into when you are done. Place the snake into the hole and push as you turn the handle clockwise. You will have to negotiate the bend in the trap, so you may think you have snagged the blockage, but in reality the corkscrew will just be pushing around the trap. When you snag the obstruction, continue turning as you pull it out.
There are times when all your efforts will result in no pay dirt. You will need to remove the toilet and snake it from the base (For removing and replacing a toilet, click here). Gently set the toilet on its side.
You could try to reach into the trap and pull out the blockage, but your hand may not get far enough (obviously, wear rubber gloves for this one). If you can't clear it with your hand, push the snake into the trap from under the base of the toilet bowl.
When the corkscrew makes its way into the bowl, tie an old rag onto it and pull it back through. With any luck, the rag will pull the obstruction out with it. This is a good way to remove things such as toys, pens, combs and various feminine products.
Until someone invents a child-proof toilet, this is a challenge that will be here for a long time. But then again, potty-training would be awfully tough.