IANAHindu, but I have some Hindu friends and just finished the Hinduism section of my Intro to Asian Relgions class, so I may be able to help out here.
It’s not quite right to think of the Hindu pantheon as being analogous to the Greek or Roman ones. Hindus worship a single, unified, monotheistic/pantheistic Godhead which they call Brahman. (Not to be confused with Brahmin, the highest class in the caste system, or Brahma, another god whom I’ll get to below.) Brahman is “ultimate reality; the eternal, unchanging essence which underlies all things,” or “the one that is not two.” The purpose of human life is to eventually see through maya, the veil of illusion, and realize your own oneness with Brahman.
Now, since Brahman has no personality or attributes, it’s hard for limited humans to really worship it. So instead, you personify the various aspects of Brahman: to worship God as the preserver you think of Vishnu, God as the destroyer of evil you think of Shiva or Durga or perhaps Parvati, etc. The trinity, or Trimurti, of Brahma/Vishnu/Shiva - Creator/Perserver/Destroyer - is important, but they’re not really the highest gods or the heads of the pantheon or anything like that. Actually, the worship of Brahma isn’t all that important in Hinduism these days - the major traditions are the Shaivite strand, which worships Shiva and his family; the Vaishnavite strand, which worships Vishnu and his various incarnations; and the Shakti strand, which worships the various goddesses. But it’s not a heirarchical pantheon like the Greek or Egyptian one - all these gods and goddesses are simply aspects of Brahman.
As to the particular goddess fecal_nugget mentioned, Durga is most commonly portrayed holding weapons in each of her 16 arms and riding a tiger, but there’s a lot of variation in that sort of thing. I believe Shiva is occasionally portrayed as female too, so there’s another possibility. Kali, who represents destruction and entropy, has four arms, but she’s almost always portrayed with dark skin.
The book we used in my class was Hinduism: A Cultural Perspective by David R. Kinsley, which I recommend to any Westerner who wants to understand the religion better.
Like I said, IANAH, so anu-la, if you want to correct anything I’ve said here, be my guest.