India actually has two monsoons -
The southwest monsoon and the northeast monsoon. The southwest monsoon, which is the main monsoon, comes in from the sea and starts making its way up India's west coast in early June. By mid July, most of the country is covered in rain. This gradually starts clearing from most places in northwest India by October.
The northeast monsoon affects India's east coast during November and December. It's a short but intense monsoon. The states of Tamil Nadu, Karnataka, and Kerala receive most of their rainfall from the northeast monsoon, while the rest of the country receives most of its rainfall from the southwest monsoon.