I have expanded my answer after seeing the comments. Hindus have many schools of thought like Sankhya, Yoga, Vedanta etc. with different concepts of God. Originally Sankhya darsana was atheist. Later on it became theist. Yoga school introduces God by hand by claiming that one of the Purushas of Sankhya is not affected by the theory of Karma. A non-Hindu might indeed become confused if he enters the dense forest of Hindu thought without the guidance of a knowledgeable person. It is better to avoid all schools apart from the Vedanta school at least at the start of one's journey. The most popular school is Vedanta and I have given below ideas about God in the Vedanta school.
The word god does not quite represent the Hindu concept of the Divine. It is better to think in terms of the Ultimate Reality which is called Brahman.
Unknowability of Brahman
Reason is strongly stressed in Hindu dharma. Hindu dharma admits, however, that Brahman is beyond reason. For example, the Upanishads say poetically,
- "The eye does not go thither, nor speech, nor the mind. We do not know It; we do not understand how anyone can teach It. It is different
from the known; It is above the unknown. Thus we have heard from the
preceptors of old who taught It to us."
(Kena Upanishad I.3-4)
- "That which cannot be comprehended by the mind but by which the mind is cognized know that alone to be Brahman, and not this that
people worship here."
(Kena Upanishad I.6)
- "That from which all speech with the mind turns away, not having reached it, knowing the bliss of that Brahman, man fears nothing."
(Taittirya Upanishad II.9)
- "He is never seen, but is the Seer; He is never heard, but is the Hearer; He is never thought of, but is the Thinker; He is never known,
but is the knower. There is no other seer than He, there is no other
hearer than He, there is no other thinker than He, there is no other
knower than He. He is the Inner Controller - your own Self and
immortal. All else but He is perishable."
(Brihadaranyaka Upanishad III.7.23)
Brahman described!
After saying that Brahman is not knowable, beyond the reach of our minds, the Upanishads describe Brahman,
- "This Self has entered into these bodies up to the very tips of the nails, as a razor lies hidden in its case, or as fire which sustains
the world lies hidden in its source...."
(Brihadaranyaka Upanishad I.IV.7)
- "It has hands and feet everywhere, and eyes, heads and faces everywhere, and It is possessed of ears everywhere. It exists among
all the creatures, pervading all. "
(Svetasvatara Upanishad 3.16)
- "He is without hands and feet, (and yet) moves and grasps; He sees, (though) without eyes; He hears (though) without ears. He knows
whatever is to be known, and of Him there is no knower. They speak of
Him as the first, the Supreme Person (Purusham mahantam). "
(Svetasvatara Upanishad 3.19)
- "You are the woman, You are the man, You are the boy, (and) You are the girl too. You are the old man tottering with a stick. Taking
birth, You have Your faces everywhere. "
(Svetasvatara Upanishad 4.3)
- "You, indeed, are the blue bee; You indeed are the green parrot having red eyes; You indeed are possessed of lightning in Your womb.
You indeed are the seasons and the seas. You indeed are without
beginning; You exist as the Omnipresent, from whom have sprung all the
worlds. "
(Svetasvatara Upanishad 4.4)
- "As from a fire kindled with wet fuel various [kinds of] smoke issue forth, even so, my dear, the Rig Veda, the Yajur-Veda, the Sama
Veda, the Atharvangirasa, itihasa, purana, vidya (arts), Upanishads,
slokas, sutras, anuvyakhyanas (elucidations), vyakhyanas
(explanations), sacrfices, oblations in the fire, food, drink, this
world, and all beings are all like the breath of the Infinite Reality.
From this Supreme Self are all these, indeed, breathed forth."
(Brihadaranyaka Upanishad IV.V.11)
Brahman known through meditation
Verses 1 to 4 suggest that Brahman is unknowable to the ordinary human mind. Then how is it possible for Upanishads to describe Brahman (verses 5 to 10)? The answer is given in the following verses,
"His form does not stand within the range of the senses. No one
perceives Him with the eye. Those who know Him through the faculty of
intuition as thus seated in their heart, become immortal."
(Svetasvatara Upanishad Iv.20)
"The wise man relinquishes both joy and sorrow having realized, by
means of meditation on the inner Self, that ancient effulgent One,
hard to be seen, subtle, immanent, seated in the heart and residing
within the body."
(Katha Upanishad I.2.12)
Human analogy and Brahman
It is clear that reason can not explain Brahman nor take us there. Then can the models of Brahman as advocated by systems like Advaita Vedanta explain Brahman? Some people say that Brahman is like a principle. If Brahman is a principle then it is hard to see how Brahman projects Itself in the human mental plane to show up as forms (Saguna Brahman). Can a mere principle project? Sometimes Brahman is also thought of as an ocean of Consciousness. This idea is baffling too. Our everyday experiences are of conscious beings. So what does an ocean of Consciousness mean?Thinking of Brahman as a principle or ocean of Consciousness is simply using analogy to our normal experience. Actually nothing whatsoever can be said about Brahman except that It exists. Let me quote Sri Ramakrishna on the nature of Brahman,
"No one can say with finality that God is only 'this' and nothing
else. He is formless and again He has forms. For the bhakta He assumes
forms. But He is formless for the jnani, that is, for him who looks on
the world as a mere dream. The bhakta feels that he is one entity and
the world as another. Therefore God reveals Himself to him as a
Person. But the jnani – the Vedantist, for instance - always reasons,
applying the process of 'Not this, not this'. Through this
discrimination he realizes, by his inner perception, that the ego and
the universe are both illusory, like a dream. Then the jnani realizes
Brahman in his own consciousness. He can not describe what Brahman
is."
"Do you know what I mean? Think of Brahman, Existence-Knowledge-Bliss
Absolute, as a shore-less ocean. Through the cooling influence as it
were, of the bhakta's love, the water has frozen at places into blocks
of ice. In other words, God now and then assumes various forms for His
lovers and reveals Himself to them as a Person. But with the rising of
the sun of knowledge, the blocks of ice melt. Then one doesn't feel
any more that God is a Person, nor does one see God's forms. What He
is can not be described. Who will describe Him? He who would do so
disappears. He cannot find his 'I' anymore."
[The Gospel of Sri Ramakrishna, October 28, 1882, p 148]
"What Brahman is cannot be described. All things in the world - the
Vedas, the Puranas, the Tantras, the six systems of philosophy - have
been defiled, like food that has been touched by the tongue. Only one
thing has not been defiled in this way, and that is Brahman. No one
has ever been able to say what Brahman is."
[The Gospel of Sri Ramakrishna, August 5, 1882, p 102]
"Brahman is beyond word and thought. It is said in the Vedas that
Brahman is of the nature of Bliss. It is Satchidananda. ..... In Samadhi one
attains the knowledge of Brahman - one realizes Brahman. In that state
reasoning stops altogether, and man becomes mute. He has no power to
describe the nature of Brahman."
[The Gospel of Sri Ramakrishna, August 5, 1882, p 102-103]
Sri Ramakrishna also says,
" Brahman is without comparison. It is impossible to explain Brahman
by analogy. It is between light and darkness. It is light, but not the
light we perceive, not material light."
[The Gospel of Sri Ramakrishna, October 16, 1883, p 307]
Then again Brahman has also been compared to a chameleon by Sri
Ramakrishna:
"Listen to a story. Once a man entered a wood and saw a small animal
on a tree. He came back and told another man that he had seen a
creature of a beautiful red color on a certain tree. The second man
replied:'When I went into the wood, I also saw that animal. But why do
you call it red? It is green.' Another man who was present
contradicted them both and insisted that it was yellow. Presently
others arrived and contended that it was grey, violet, blue and so
forth and so on. At last they started quarreling among themselves. To
settle the dispute they all went to the tree. They saw a man sitting
under it. On being asked, he replied,'Yes, I live under this tree and
I know the animal very well. All your descriptions are true. Sometimes
it appears red, sometimes yellow, and at other times blue, violet,
grey, and so forth. It is a chameleon. And sometimes it has no color
at all. Now it has a color and now it has none.'
In like manner, one who constantly thinks of God can know His real
nature; he alone knows that God reveals Himself to seekers in various
forms and aspects. God has attributes; then again He has none. Only
the man who lives under the tree knows that the chameleon can appear
in various colors, and he knows, further, that the animal at times has
no colors at all. It is the others who suffer from the agony of futile
arguments........ God reveals Himself in the form which His devotee
loves most."
[The Gospel of Sri Ramakrishna, October 28, 1882, p 149]
I am adding this to clear up confusion. Although I am afraid that it might increase it!
Nirguna Brahman does not exist. It is Satchidananda. Here Sat means existence itself, chid means consciousness itself and ananda means bliss itself. It is impossible to say anything about Brahman.
The Upanishad also says that Brahman is pure consciousness, devoid of
other aspects contrary to this, and without any distinguishing
features, as in, “As a lump of salt is without interior or exterior,
entire, and purely saline in taste, even so is the Self without
interior or exterior, entire, and pure Intelligence alone”
(Brhadaranyaka Upanishad IV.v.13), which means that the Self has no
internal or external aspect apart from pure consciousness, Its nature
being mere impartite consciousness without any interstices. Just as a
lump of salt has the saline taste alone both inside and outside, and
no other taste, so also is this Self.
Brahma Sutra Bhasya of Sri Sankaracharya III.ii.16
Nirguna Brahman can only be expressed in negation.
Moreover, the Vedas reveal through a negation of other aspects that
Brahman has no distinguishing feature, as for instance in, “Now
therefore the description (of Brahman): ‘Not this, not this’”
(Brhadaranyaka Upanishad II.iii.6), “That (Brahman) is surely
different from the known; and, again, It is above the unknown” (Kena
Upanishad I.4), “That Bliss of Brahman, failing to reach which, words
turn back along with the mind” (Taittiriya Upanishad II.ix.1), and so
on. And it is also known from the Vedic texts that Badhva being asked
by Baskali, replied merely by not uttering a word, as stated in, “He
(Baskali) said, ‘Teach me Brahman, sir.’ He (Badhva) became silent.
When the question was repeated a second and a third time he said, ‘I
have already spoken, but you cannot comprehend. That Self is
Quiescence’ “. Similarly in the Smritis, the instruction is given
through a negation of other things, as in, “I shall tell you of that
which is to be known and by knowing which one attains immortality. The
supreme Brahman is without any beginning. It can neither be called
gross (visible) nor fine (invisible)” (Gita XIII.12), and so on.
Similarly the Smriti mentions how Narayana in His cosmic form said to
Narada, “O Narada, that you see me as possessed of all the (five
divine) qualities of all elements, is only because of My Maya, called
up by Myself. For else you should not understand Me thus.”
Brahma Sutra Bhasya of Sri Sankaracharya III.ii.17
Brahman according to Yajnavalkya
Yajnavalkya said: O Gargi, it is the supreme being that the non-yogins
call gross but, in fact, that is eternal and wonderful lord; one that
is not long, not red, that has no head, that has no setting, hence
that has a lasting taste, that has no contact, no smell, no juice, no
eyes, no ears, neither speech nor mind, no brilliance, no proof [or
magnitude], no (worldly) happiness, no name, no race, no death, no
age, no ailment; that is nectarine, that is expressed by the word Om,
that is immortal, that has neither a predecessor nor a successor, that
is endless and non-external. It eats something. It does not eat
anything. ..
Linga Purana II.9.53–54
Brahman does not exist but is the source of all existence. Brahman, however, cannot be described in any manner.
Where does Shiva, Vishnu come in?
Special Forms
Brahman also maintains special forms for helping human seekers. The various deities like Siva, Vishnu, Devi, Ganesha etc are different names and forms of Brahman. In spite of these Devatas Hinduism is not polytheistic as is clear from the following passages:
"Know that this entire universe is under the control of one divine
Being. The Veda that is in the soul.......regards the unity of various
creatures. When a living creature realizes this unity in consequence
of true knowledge, he is then said to attain to Brahman".
Mahabharata Santi Parva Section CCLXXX
" The Supreme Spirit hath three condition, In the form of Brahma, he
is the Creator, and in the form of Vishnu he is the Preserver, and in
his form as Rudra, he is the Destroyer of the Universe".
Mahabharata Vana Parva Section CCLXX
This one divine being is called Isvara and the multiple Deities are His forms. Brahman is called Isvara when thought of as relative to the universe.
