After the Cuban Revolution, how did Cuba rebuild its government in the 1960s?

After the Cuban Revolution, Cuba (or Fidel Castro) tried
to rebuild the government by creating a vanguard communist party that would serve as the
effective leaders of the country.

Before and during the
revolution, there had been many different groups that had opposed Batista.  After the
revolution, Castro unified these groups under his own leadership.  By 1965, these
organizations had been become the Communist Party of Cuba.  This party was the real
government of Cuba.

So, the basic process was one of
amalgamation of the revolutionary groups that had opposed Batista.  These groups were
combined into a communist party which took control over all major groups in society such
as labor unions.  It used its control over these groups to give it enough power that it
essentially became the government of Cuba.