Two types of products used to clear a clogged toilet are a plunger or a closet auger. A plunger should do the job for moderate clogs, but a closet auger might be necessary for clogs that are severe.
Like a snake that clears out other types of drains, a closet auger has a crank and a cable, but it fits the contours of the toilet bowl.
Another product to use to clear a clogged toilet is dish soap. Sometimes a clog in a toilet clears after pouring dish soap down the toilet and then flushing the toilet with hot water.