Full answer
The right plunger matters more than most people realize. A cup plunger (flat bottom) is designed for sinks and tubs; a flanged or ball plunger has a rubber flap that fits into the toilet drain opening and creates a much stronger seal. Using the wrong type is the most common reason plunging fails.
Before plunging, check the water level in the bowl. If it's about to overflow, do not flush again. Instead, remove some water with a bucket to give yourself working room. Add hot (not boiling) water from the tap to help loosen the clog — the heat softens most organic material.
Position the plunger so the flange inserts into the drain and the cup forms a complete seal. Push down slowly on the first stroke to expel air, then pump 6 to 10 times with sharp upward pulls before breaking the seal. The suction is what clears the clog, not the downward pressure. Repeat 2 to 3 cycles if the first doesn't work.
If plunging fails after several attempts, try the dish soap method: squeeze a generous amount of dish soap into the bowl, wait 10 minutes, then add a bucket of warm water poured from waist height. The soap lubricates the clog and the rushing water adds force. A drain snake (toilet auger) is the next tool if this also fails — it physically breaks up or retrieves the obstruction.