The name 'Hinduism' is of a much recent origin, coined by the Greeks and Arabians to refer to the religion of the people living around and to the East of the river Indus. The earliest records of this religion are in the Rig Veda, the oldest known human literature. Some portions of the Rig Veda have been dated to before 6000 BC. This implies that the religion was in vogue atleast a few centuries earlier than that. Hinduism has been gaining increasing popularity due to its high philosophy, broad outlook and non-dogmatic approach. Hinduism is different from many other religions in that it does not have a founder and does not claim exclusivity. It explicitly accepts all religions as valid.
Lord Krsna says in Bhagavad-gita (7.8), pranavah sarva-vedesu: 'In all the Vedic mantras, I am represented by pranava, or omkara.' Thus chanting of the Vedic mantras beginning with omkara is directly chanting of Krsna's name. There is no difference. Whether one chants omkara or addresses the Lord as 'Krsna', the meaning is the same, but Sri Caitanya Mahaprabhu has recommended that in this age one chant the Hare Krsna mantra (harer nama eva kevalam). Although there is no difference between Hare Krsna and the Vedic mantras beginning with omkara, Sri Caitanya Mahaprabhu, the leader of the spiritual movement for this age, has recommended that one chant Hare Krsna, Hare Krsna, Krsna Krsna, Hare Hare. Hare Rama, Hare Rama, Rama Rama, Hare Hare. (from Bhaktivedanta Prabhupada Commentary, Srimad Bhagavatam 6.5.26)
The answers to these questions are refered in the other answers. So please read these before the other questions, even if you are familiar with Hinduism and Lord Krishna.