The best way to unclog a slightly blocked toilet pipe is with a plunger and by adding dish soap into the water. The plunger uses suction to create pressure within the pipes, which can help to break apart the clog and push it through the pipes. The dish soap helps to lubricate the blockage and break down fats and grease. For tougher clogs, you may need to use a toilet auger or snake. This tool inserts a long, flexible cable into the pipes and uses a crank to move the cable through the pipes and break apart the clog.