Essentially, Robert Mugabe came to hold the amount of power he now has through the corrupt use of political power. Mugabe first came to power through democratic means, but he then used the power that he had to take still more power until he eventually came to have dictatorial powers over Zimbabwe.
Mugabe became active in politics in the early 1960s, decades before Zimbabwe became independent. He eventually rose to be the leader of one faction of the black Zimbabweans' movement for independence. His faction was called the ZANU. When elections were finally held in 1979, Mugabe's faction won the majority of seats and Mugabe became Prime Minister. By 1987, Mugabe was President and has held that position ever since.
Once Mugabe became President, he used his political powers to chase his rivals out of the country and to oppress those who stayed. This eventually allowed him to become the a dictator.
Please follow the links below for much more detailed information -- especially the salem-history link.