There are at least two ways in which to answer this. One has to do with the theory of communism. The other has to do with the practice of that system in the world so far.
In theory, no one governs in communism. In communist theory, the government eventually withers away and disappears. This happens because the proletariat wins the class struggle and society reaches a point where everyone is in agreement as to how it should be run. There would be no need for a government to force people to act in the right way as they would do it because of their beliefs. Thus, we can answer this by saying that no one governs in communism.
In practice, however, no country has reached this stage. In communist countries, the communist party has ruled. More specifically, communist parties, typically controlled by a single person, have ruled. In communist countries, the government is run by the communist party. This has been true of countries such as China, Cuba, and the Soviet Union. In these countries, there has typically been one person who has dominated the party at any one time. Thus, in the real world, communist countries have been governed by communist parties headed by a person (such as Stalin, Mao, or Castro) who could hold almost dictatorial powers.