The British took over India due to the vast commercial and financial interests and opportunities within the region. In 1757 the British East India Company defeated Newab of Bengal, effectively bringing to the region not only British commercial power, but British military power.
Following the loss of the American Colonies, British imperialistic sights looked towards the Far East, and India provided a great deal of wealth for Britain. The British East India Company had control of the most favorable trade routes to the region, and a Royal Charter meant the company had a monopoly on all trade there. Britain gave the company governing power over India and helped supply troops and resources.
The East India Company was also able to effectively withstand constant military attacks from local tribes, as the region's people were unable to fight a united front, and the company had acquired a private army of local Indian people who were loyal to British interests.
In the mid-19th century, the company's power faded after an armed rebellion against the British occupation and influences in the region. Instead of leading to Indian independence, the rebellion resulted in Britain taking direct control of India, which lasted all the way until 1947.