First of all, Hinduism is not a religion as we tend to think of a religion. It is a name given to a range of practices, attitudes, beliefs, schools of thought, and the social and political systems connected to these. There is in Hinduism the idea of an enduring divine reality that never changes: Brahman. And “God” is the personalized form or manifestation of that ultimate divinity and takes many forms.
Interestingly, the Deity in Hinduism has a triple-form, and thus a certain resonance with Christian belief in the Trinity. There is Brahma, the Ultimate Reality, associated most with the transcendence of the Divine, remaining somewhat in the theological background as the revered but disengaged Creator.
Then there is Shiva, who reflects more the immanence of the Divine and who exemplifies divine androgyny in Hinduism. All name-forms of deities have female counterparts or consorts. Shiva’s feminine aspect takes the names and forms of the lovely Parvati and the ferocious Durga. Devotees are known as Shaivites.
Finally, there is Vishnu, who appears as both helper and savior. Devotees (Vaishnavites) celebrate his ten most famous avatara or incarnations. Two of the principal avatars of Vishnu—Rama and Krishna—come to save humankind from immorality and to punish evildoers.
But since human is already essentially divine, they do not assume the human condition in order to divinize it, but to rescue it from the powers of evil. The Upanishads (writings that form the basis of much of Hindu philosophy) identify an animating principle, atman (similar to “soul” in Christian understanding), with the larger spiritual reality called Brahman. Whereas a Hindu might thus say, “I am God,” or “Thou art That”, a Christian would say, “I can share God’s life, but I am not God.”
Hindus also believe that the effects of actions (karma) become attached to one’s “self” (atman) and must be stripped away. The results of these actions are like a spiritual substance which entrap the self in the body. Liberation from the body is the only way out. The focus is upon the atman/soul, and there is no salvation accorded to the body as in Christian faith. Until the negative effects of karma have been neutralized by transcending selfishness in one’s actions, atman will go through a cycle of rebirth or reincarnation. In Christian understanding, Christ has in effect redeemed us/set us free from the effects of sinful behavior, and we have only one life.
Other differences:
There are two categories of scripture: Sruti (divinely inspired, e.g. the four Vedas) and Smrti (“remembered scriptures” which contain laws and stories like the Ramayana and Mahabharata).
There is no overarching institutional structure for safeguarding orthodoxy. As a result, people choose one name-form of the divine or one set of narratives about the deity over others, influenced by regional religious heritage.
There are many levels of heaven and hell, and they are all intermediate stops on the long journey to freedom from rebirth when at last the atman becomes one with Brahman.