Khazâd is the name the Dwarves in J.R.R. Tolkien's universe use to describe themselves. It is one of the few words of the Khazâd language known to non-dwarves.
The dwarves were crafted by the Vala Aulë, the Vala of blacksmithery and craftwork, during the really early years (aeons prior top the awakening the elves, and even more aeons before the awaking of the Edain (i.e., the race of men; the dawning of the First Age)); and by all accounts before the dawning of the Years of the Trees, the time immemorial before the First Age of the world), before the sun and moon rose, before the Tolkien's Quendi awoke, some three thousand years prior to the dawn of the First Age. He did this in secret, hiding his work from Ilúvatar. Since he could not imbue his creations with the spark of life, they wandered aimlessly Beleriand and the caverns beneath the White and Blue Mountains (as dwarfs, since the dawn of their race, have saught out underground refuge, in accordance with the prediliction for caves and the like), most noted to be Khazad-Dûm around like twelve clockwork puppets.
Of course, you can't hide from an omniscient god (.e.g, Ilúvatar). Eru confronted Aulë. Unlike Melkor, Aulë repented of his sin and tried to smash the puppets. Eru stopped him, instead giving them life. But since the Quendi were already scheduled to be the First Children, and the Edain the Second Children, Eru put the Khazâd to sleep, to awaken at an undertimined time, which seems to be shortly after the Quendi around the down of The Years of the Trees (viz., approximately 2,000 years prior to the beginning of the First Age, during which Eru hung back for a few thousand years, attempting to come with a solution that would be beneficial to all concerned.).
The seven lines of Dwarves each trace their lineage to one of the seven Fathers. The most famous lineage is that of Durin, who resided in Khazad-dûm. Durin himself died mid-way through the First Age, despite his royal title, "During the Deathless," he died sometime between the latter half of the First Age, and his "Deathless" title was descended until the dwarven race gradually faded from the annals of Middie-Earth. His last known descendent was Gimli, elf-friend, surviving member of The Fellowship of the Ring, and son of Glòin, who ended up, by Tolkien's own accounts, to be the last of the Khazâd; he, along with his great friend, the Silvan elf Legolas Greenleaf, departed the newly-renamed Eryn Lasgalen (formerly Mirkwood, land of the wood elves) together for Valinor, whereafter he (presumably) lived happily ever after in Valimar (the central plains of Valinor) with Legolas, thus becoming the first, and as far as most Tolkin scholars are concerned, the only dwarf ever to set foot in Valinor, much less reside there permanently. Gimli, whose date of death is never established by Tolkien, can either be assumed to have died of natural causes (he was approximately 250 years old when he sailed to Valinor with Legolas), or that the Valar granted him immorality, like the elves, to live out the rest of his eternity among the Valar and the elves. What became of him after that, Tolkien left to his readers' imagination.
The Khazâd are responsible for the creation of the ents (although this is disputed; [The Encyclopedia of Arda attributes this feat to the Quendi, the first of the elves, to be responsible for ent-speech). When Aulë's wife, Yavanna, found out how much havoc would be caused by dwarven axes, she asked for a guardian of the Kelvar and Olvar to be created, as well.
Questions about when they woke up, and who the Fathers mated with, or indeed whether Khazâd engage in sex, are not answered in the text of any of Tolkien's books. It is never determined by Tolkien, or his son Christopher Tolkien, or, indeed, any other member of the Tolkien clan, whether the Khazâd ever actually engaged in sexual procreation; although in the movie adaption of The Two Towers Gimli makes a point in conversation with Éowyn that dwarven sexual procreation does, indeed, occur (if rather obliquely, by extolling the virtues of dwarven women); witness his horseback conversation with Éowyn about the origins of newborn dwarves and his sarcastic postulate that dwarves simply "spring up out holes in the ground," which, while it could be considered filmmaker liberty, is the closest we've got to ascertaining the dwarven birds and bees, if you catch my meaning. Also, it could be an expansion of the Aulë theory of dwarven procreation (that is, that dwarves are not born, per se, but that each one is indivually created by Aulë), which Tolkien, sadly, fails to go into much detail during his descriptions.