To make the unclogging process easier, remove as much quantity of water from the toilet bowl as possible. Cover your hands with a pair of rubber gloves and use a foreign object to bail out water and pour it into a large container. Take the large container to your garden, dump its contents and then discard both the gloves and the container. Leave the toilet as is for about 10 to 15 minutes.
You will now need to break the solids clogging the toilet into smaller pieces. Use something about the size of a serving spoon for this purpose. It would be best if you can fish any solid waste from the toilet. Be sure to properly discard the object you used for breaking up the solid waste.
Add warm water to a large soda bottle until full. Wear another pair of rubber gloves, place your thumb over the opening of the soda bottle and then drive the bottle opening all the way to the bottom of the toilet. Apply pressure on the bottle with your hands and simultaneously take off your thumb. Warm water will shoot out of the soda bottle and into the toilet drain and dislodge the clog.
Possible overflows can be dealt with by placing towels around the toilet. Flush the toilet to check if it is unclogged. If not, you will have to repeat all three of the above steps.
Add about three quarts of water to a small container and boil over a stove. Carefully carry the water all the way to the bathroom and pour it directly into the toilet for as high a point as possible. Be careful because water may splash back or overflow. Allow about 15 to 20 minutes for the water to cool down and flush the toilet one more time.