Question
How did the Vedas in Hinduism come into existence?
Answer
The Vedas are Śruti, which means "that which is heard" (what Christians would call "revelation"). Hindus believe that from time immemorial, sages known as Dhrishtas (literally "seers") have, during a state of Tapasya (deep meditation), heard sacred verses directly from the gods. In the Dwapara Yuga (the age before the one we're currently in), these verses were compiled by a sage named Krishna Dwaipayana Veda Vyasa (or Vyasa for short) into a set of four books we call the Vedas. (Technically Vyasa only compiled the first three books - Rig, Yajur, and Sama - while the Atharvana Veda is attributed to the sages Angiras and Atharvan.) As the words of the Vedas are believed to be divine in origin, they are held to be the foremost authority of the Hindu religion. As Rama says in the Ayodhya Kanda of the Ramayana, the Vedas "have the foundation in Truth [and] one should thoroughly surrender to truth."
I should add that each of the four Vedas is divided into four portions: Samhitas, the core part of the Vedas which consist of hymns to various gods; Brahmanas, which provide instructions on the proper conducting of important rituals; Aranyakas, which provide a guide to rituals meant for forest-dwellers and hermits; and Upanishads, which consist of conversations between teachers and students which clarify the philosophical message of the Vedas. In any case, when someone says "I read the Rig Veda" without qualification, they usually mean the Rig Veda Samhita, because the Samhitas are the core part of the Vedas which came directly from the gods.
(Note: the above is excerpted from my answer here.)
As for where you can read the Vedas, sacred-texts.com is a good site. Here's the Rig Veda Samhita, the Krishna Version of the Yajur Veda Samhita, the Shukla version of the Yajur Veda Samhita, the Sama Veda Samhita, the Atharvana Veda Samhita, the Shatapatha Brahmana of the Yajur Veda, some major Upanishads from various Vedas, and some minor Upanishads.
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