Dharma

"Then was not non-existent nor existent: there was no realm of air, no sky beyond it.
What covered in, and where? And what gave shelter? Was water there, of unfathomed depth?
Death was not then, nor was there immortality: no sign was there, the divider of day and night.
That one thing, breathless, breathed by its own nature: apart from it was nothing whatsoever.
Darkness there was: at first concealed in darkness, this all was indiscriminated chaos.
All that existed then was void and formless: by the great power of warmth was born that singularity.
Thereafter rose desire in the beginning, desire the primal seed and germ of spirit.
Sages, who searched with their hearts, discovered the existent’s kinship in the non-existent.
Transversely was their severing line extended: what was above it then, and what below it?
There were begetters, there were mighty forces, free action here and energy up yonder.
Who verily knows and who can declare it, when was it born and whence comes this creation?
The gods are later than this world’s production. Who knows then when it first came into being?
He, the first origin of this creation, whether he formed it all or did not form it,
Whose eye controls this world in highest heaven, he verily knows it, or perhaps he knows it not" - Rig-Veda 10.129.7

As a Hindu i am occasionally asked by other people and even often ask myself whether i believe in Hinduism. After giving it much thought, i always end up finding this question perhaps somewhat of a misunderstanding of such a vast, diverse religion and to me personally irrelevant.
But to answer the question in a round about way i usually like to say that the core aim of Hinduism and therefore a Hindu is to acquire the truth and since Hindu's believe there are many paths to the truth, there's no need for one to have blind faith or devotion in any particular one, not that one necessarily cant or shouldn't.
An invocation in the Upanishad says...

"Truth alone triumphs, not untruth.
Lead me from the unreal to the Real.
Lead me from darkness to Light.
Lead me from death to Immortality".

What make Hinduism so unique among world religions is this intrinsic philosophical realisation that there are many paths to the Truth / God, which can be summed up in its central motto "let noble truths come from all directions".

If you happen to deny the existence of God, that's fine too, Hinduism has always accommodated if not necessarily accepted such alternate views (Nastika) as exemplified by Buddhism and Jainism. In fact, within Hinduism and Ancient India there have been many atheist schools of thought such as Charvakanism that strongly advocated materialism and rational thought as can be seen in their following exhortation...

"While life is yours, live joyously;
None can escape death's searching eye:
When once this frame of ours they burn,
How shall it ever again return".

Unlike the 3 major monotheistic Abrahamic religions, Hinduism is unique in that it doesnt claim to have a monopoly on the Truth / God.
Like other Eastern religions, Hinduism is a philosophical religion that is the sum of Indian religious thought, practice and tradition for over that last 5,500 years and as such is the worlds oldest continually existing religion.
It has no founder, no one supreme holy texts but rather several of them and no set definition of what it means to be a Hindu. At the same time, Hinduism is much more than just merely a religion, it is also synonymous with Indian culture and civilisation.

Hindu scriptures and most Hindus generally agree on the existence of one supreme impersonal divine being (Brahman) that can be worshipped in many forms, thus explaining the proliferation of the numerous personal deities (devas) that most non-Hindu's are familiar with when they think about our religion. To Hindu's it matters not how many or to which God one prays to, God can be reached through whichever way is endearing to the believer so long as its sincere.
A popular Hindu invocation says...
"O Lord, please forgive three sins that are due to my human limitations:
Thou art everywhere, but I worship you here;
Thou art without form, but I worship you in these forms;
Thou needest no praise, yet I offer you these prayers and salutations.
Lord, please forgive three sins that are due to my human limitations".

Nevertheless there are still four principle orthodox ways of achieving union (Yoga) of the soul (Atman) which is the body's immortal nectar (Amrit) with God (Brahman) and therefore liberation (Moksha / Nirvana for Buddhists) from the cycle of death and rebirth (Samsara) and thus the illusion (Maya) of our perceived reality as opposed to our supreme cosmic reality. These ways are Bhakti Yoga (the path of love and devotion), Karma Yoga (the path of right action), Raja Yoga (the path of meditation) and Jnana Yoga (the path of knowledge and wisdom).

These are complemented by the four stages of human life: Brahmacharya (Student Life) where one acquires knowledge, self discipline at the feet of a Guru (Spiritual Teacher) and learns to live a life of Dharma (Righteousness) , Grihastha (Household Life) where one fufils ones duty to family and society, Vanaprastha (Retired Life) where one gradually withdraws from the world and freely shares wisdom with others, Sannyasa (Renounced Life) where one completely renounces the world and dedicates themselves to spiritual pursuits.

While one is free to follow any path they choose in Hinduism, this sometimes can lead to a problem Tagore observerd in a conversation with H.G. Wells, namely that there is too much religious tolerance in India, so much so that any sort of injustice can be perpetrated in the name of religion, whether it is the ridiculous rules and practices of the Brahmin caste system or the brutalities inflicted by a particularly nasty foreign arab religion that continues to this day, without the majority hardly stopping to bat an eyelid.

Though Hinduism much like India itself has always at its own pace changed with the times as is indeed happening today, nonetheless some purposeful housecleaning is obviously in order and gradual reforms brought about through greater social consciousness/activism and community outreach are what is needed to keep our great Hindu tradition strong.