Start with dish soap
As soon as the toilet clogs, head to the kitchen and fetch some dish soap; the slippery soap should help lubricate the clogged pipe and allow the lodged debris slide down more easily. Pour about a half-cup into the toilet. If you haven't got any dish soap on hand, chop a bar of soap into small chunks and drop the pieces into the toilet.
Add hot water
If dish soap alone doesn't do the trick, adding water might move things along. Fill a bucket with hot bath water (boiling water could cause a porcelain toilet to crack), and pour the water into the toilet from waist level. The force of the water could dislodge whatever is causing the clog.
DIY a drain snake using a wire hanger
A more severe blockage could require manually moving the item. To do this, unravel a wire coat hanger until it's straight. Push one end of the wire into the clogged area. Prod the debris until it becomes free and flows down the drain. (Related: Here are more genius uses for your extra coat hangers.)
Try this mixture
As an alternative to using dish soap, try this all-natural solution: Pour 1 cup baking soda and 2 cups vinegar into the toilet. Allow it fizz for a half hour. If clog doesn't dissipate, try the hot water trick.
Use a plastic bottle to create water pressure
Warning: This trick could get messy. Start by removing as much water from the toilet bowl as possible (you can do this by repeatedly filling a small container with toilet water and pouring the water into a bucket). Next, fill a large plastic bottle with warm water. Place your thumb over the top of the bottle, and fit the top end of the bottle into the outlet at the bottom of the toilet (you'll want to wear rubber gloves for this step). Remove your thumb and squeeze the bottle so the water inside shoots down the pipe. The added pressure could dislodge whatever was causing the clog. (Related: Are you hanging your toilet paper wrong?)