Napoleon first came to a position of great power through his participation in the coup d'etat of 19 Brumaire. He then solidified and extended his power through the use of plebiscites.
Before 1799, Napoleon was the major military leader of France, but he did not have a huge amount of political power. In that year, however, he joined the Abbe Sieyes, who was an important political figure, in a coup. Sieyes thought that he could use Napoleon's military prowess and his popularity to help support the government while keeping power for himself.
But this plan would not work. Napoleon had more ambition than that. He used plebiscites to show his popularity among the people and to force himself into positions with greater power. The most important plebiscite was the one that took place in 1802. That plebiscite gave Napoleon the title and power of "Consul for Life." At that point, Napoleon's rise to power was essentially complete.
After the French Revolution installed a Republic as the government in France, other European countries and their monarchs launched invasions against the French. This is how General Napoleon Bonaparte came to power in the French military. Even though he had lost some campaigns in Egypt, Napoleon was overwhelmingly popular in France because of his victories against Austria and Italy. In 1801, when Britain allied with Russia and Austria, the French government was in crisis. This allowed a takeover- the coup d'etat.
Napoleon came back to France and helped stage a coup d'etat (an overthrow of the government/regime, usually though not necessarily violent). After successfully overthrowing the Republic, Napoleon became first consul of Rome (a title that echoed back to the Roman Republic). A year later, he became consul for life. Shortly afterwards, a plebiscite (a direct electorate vote) was held and Napoleon was made Emperor of France. As Emperor, he centralized government, created the Bank of France, brought back Catholicism, and formed law with the Code Napoleon.