Pakistan had it’s first general elections in 1970. Awami League, a party that was in strong favour of East Pakistan’s right to self-govern won a majority (167 of 169 seats). The inaugration of the new Assembly based on the election results was postponed on veto by Pakistani military brass.
This led to strikes in East Pakistan and riots targeting people who suppoerted the West Pakistan government in the elections.
By the end of August 1971, there were more than 8 million East Pakistan refugees in India, most of them Hindus. The Indian government followed an open-door policy, anyone who came was allowed in.
India was hosting training camps for Bengali guerillas by the summer of 1971.
The US (under Nixon) was pretty anti India because of Indian actions during this time.
On 3rd December 1971, Pakistani bombers attacked airfields in India on the western border. Indira Gandhi said that this amounted to a declaration of war and India retaliated with massive air strikes.
The Indian army moved towards Dhaka from multiple directions. The civilians helped Indian efforts as there was massive anger against West Pakistan. On 6th December, the government revealed that they support the creation of a new nation to replace East Pakistan and recognized the Provisional Government of the People’s Republic of Bangladesh.
On the 16th of December, the Indian army accepted a signed instrument of surrender from General Niazi in Dhaka.