Communist leaders can be chosen in various ways, but they are mostly self-appointed through political revolution. Notable communist leaders like Vladimir Lenin of Russia and Mao Zedong of China seized power by force. According to the Manifesto of the Communist Party by Karl Marx, workers should take power from the upper classes, leading to a dictatorship of the proletariat.
The Communist Manifesto's call for a dictatorship of the workers is one of the primary reasons why most communist revolutionaries take the reigns of authority without consent. With that being said, communists can also be chosen through election or succession.
According to a profile from the BBC, North Korea became a communist dynasty when former leader Kim II-sung died in 1994, with his son, Kim Jong-il, immediately succeeding him. In other cases, communist leaders can be elected, if they choose to campaign in traditional political systems. There are communist parties around the world that compete with other political parties for election.
An article from the Free Republic highlights the fact that communists often campaign through democratic electoral means to instill revolutionary change once elected.