I have tried to answer this question as succinctly as possible, while not leaving out significant points. It is however a deep issue and this answer is a bit more detailed than you may have been hoping for. If its too much information, or not enough, please feel free to let me know. I can easily simplify or expand it.
What God is, especially for Hindus, requires study and time to understand. It is well worth the effort! I will attempt to summarize it for you here. Again, if you wish more information or clarification, feel free to write back.
From the earliest Aryan periods of Hindu thought, the existence of God has been present. People usually credit Abraham as the father of monotheism (the worship of a single God), however the Indian Vedas (books of knowledge) taught it long before the biblical Abraham was born.
As we read in the Brihadaranyaka Upanishad 3.9.1:
"Then Vidaghdha, son of Shakala, asked him, "How many gods are there, Yajnavalkya?" Yajnavalkya, ascertaining the number through a group of mantras known as the Nivid, replied, "As many as are mentioned in the Nivid of the gods: three hundred and three, and three thousand and three."
"Very good," said the son of Shakala, "and how many gods are there, Yajnavalkya?"
"Thirty-three."
"Very good, and how many gods are there, Yajnavalkya?"
"Six."
"Very good, and how many gods are there, Yajnavalkya?"
"Three."
"Very good, and how many gods are there, Yajnavalkya?"
"Two."
"Very good, and how many gods are there, Yajnavalkya?"
"One and a half."
"Very good, and how many gods are there, Yajnavalkya?"
"Ek [one]."
So, what of the other "three thousand, three hundred and five" gods? [some say even more]. Here is where we find the heart of Hindu theology.
First, we must understand that Hinduism is not a single religion like Christianity, Judaism, Islam and so on, it is the composite of many different religious traditions melded into unity. These diverse religions, when taken as a group, are known as the Sanatana Dharma or Universal Truth or Way. The name "Hinduism" is a slang term that has generally been
accepted as though this were a single religion.
"Hindus" differ one from another in many respects and the principle deities they worship have shifted and transformed as well. Today, the majority of Hindus worship "forms" of Vishnu/Narayana, Siva, or Devi -- generally speaking.
Most Hindus conceive of God in transcendence, which is to say, they readily acknowledge that the specific names and forms attributed to "God" are but limited conceptions of That Which Is Beyond.
Many Hindus worship various forms of Visnu/Narayana such as Krsna (Krishna) or Ramacandra. They follow the teachings of scriptures such as the Mahabharata, the Srimad Bhagavad Gita (read my free online translation at: http://www.allfaith.com/Religions/Hinduism/gita.html), the Ramayana and so on.
Others conceive of God in forms of Lord Siva (Shivah) and his consort Parvati, and revere scriptures such as the Tirukural ( http://en.wikipedia.org/wiki/Tirukkural )
Others worship the Goddess (Devi) in various forms, as Kali, Durga, etc. and read scriptures such as the Devi Gita and so on.
These of course are only the more significant divisions.
In popular Hinduism (i.e. as commonly practiced by the people), most honor all the various deities. Families tend to have what is known as an ista devata or familial "house god" that is honored. For instance, a Vaisnava worships Lord Vishnu, however at home he/she might specifically worship Lord Jagannatha due to tradition or some specific event in his or his family's past.
Despite this, the concept is generally held in mind, even if it is not voiced, that, as the ancient Rg Veda says, "Truth is one, the sages merely call it by different names."
For one who principally worships Lord Siva for instance, the worship of Lord Visnu is not problematic. There may be some "sibling rivalry" that argues that Siva is higher than Visnu or vice versa, but in the end, Hindus believe that Truth is One.
Then there are demi-gods (or lesser gods) who fulfill specific "functions," for instance, when beginning some new undertaking both Vaisnavas, Sivaites and worshippers of the Great Goddess will often invoke the blessings of Lord Ganapati (the elephant-headed Lord Ganesha, son of Lord
Siva and Goddess Parvati).
For most Hindus, the identity of "the ultimate God" is not what matters and is sledom discussed or even considered. The important thing is what we might consider "spirituality" or the living of a spiritual life. Hindus understand that God looks beyond all superficialities and personal
preferences.
Then there is the arguably more philosophical side of Hinduism, often referred to as Vedanta, or the "End of the Vedas." Masters such as Srila Sankara (circa 800 CE) developed the Path of Impersonalism, wherein the
various deities are seen metaphorically rather than as literal gods to be worshipped.
It is argued that this doctrine arose in India as a reaction to Buddhism. Those who adopted this view felt that the religions of the Sanatana Dharma had developed into superstitions and vain traditions, that they had lost their spiritual potency. They blamed this development, and the
perceived corruption of the brahminical hierarchy, for the rise of the Buddhadharma (Buddhism) in India (circa 5th century BCE to the time of Sankara) that threatened to destroy traditional Hinduism. This view seeks to filter out all cultural influences and achieve the distilled wisdom of the Vedas (i.e. the 'end of the Vedas') in its pure form.
While the majority of religious Hindus continue to worship the ancient gods and goddesses, this movement, thanks to masters such as Srila Ramakrishna and so many others, has been incorporated into popular Hinduism, giving it a more eclectic and universal appeal.
Rather than the heavenly "pleasure groves" of the spiritual world sought by "personalist" Hindus, the "impersonlists" seek a unified field of being that is practically indistinguishable from the Buddhist Nirvana
(for this reason, many people consider Shankaracharya a "closet Buddhist"). For the personalists, the neti-neti or Not-this Not-that state of being attained by this impersonalist samadhi (in "nirguna Brahman"), is
but the shining effulgence of the Personality of Godhead.
Hence, within Hinduism, there is room for both personalist and impersonalist approaches. Hinduism is all-inclusive. Indeed, all religions of the planet technically belong to the Sanatana Dharma as all are seeing
the Universal Truth!
Here is the essential difference between these two views:
Material reality is said to be "saguna". This is to say, "sa" or with and "guna" or qualities, seperate existence. For Personalists, upon moksa or liberation, the atman (the individual self or being or "jiva") continues to exist in the presence of God, the Paramatman ("param" highest, "atman" Self or Being). Material existence is real, but temporary. Spiritual reality is real and eternal.
For Impersonalists, material nature is not real but illusion (or maya). These "Mayavadis" (affirmers of the doctrine of the illusion of manifest existence) believe that upon moksa (liberation) the atman (as the falsely perceived individual self) awakens to the truth that everything is oneness, not-this, not-that or neti-neti, and utterly beyond all duality. The material multiverse is hence deemed an illusion, a dream from which the jiva (self) awakens at liberation (as the Self).
From this perspective then, there is still "God," but God is not a differentiated being, a param-atman (an individual, even if Supreme, Self or Being), but the non-differentiated totality of awareness/existence. Again, essentially the same as in Buddhism.
This is obviously a very deep and complex subject and I have only scratched the surface with this answer, but I never know how much detail people want. If this does not suffice, I do hope you will feel free to inquire further.
Om tat sat,
~John of AllFaith
Jagannatha Prakasa