hm i know where they live, cant remember the name, but i know how they came to be
illuvatar had promised his children to the world (the elves) but one of the valar grew tired of waiting and created his own people (dwarves) but illuvatar but the dwarves into a sleep until the elves entered middle earth
in the 3rd age, there are many dwarves in the iron hills far far to the north, at the lonely mountain next to dale and laketown of the humans (important place in the hobbit, and where smaug used to live after he kicked out the dwarves and then got kicked out in the hobbit, permanently, if u know what i mean), and also in mountain ranges far to the west, where they spent their time mining and basically avoiding the growing evil during teh time of the lotr.
well the dwarves in erebor werent idle during the wars. sauron when he attacked minas tirith he attacked everywhere, lorien, mirkwood, and the lonely mountain. all in an effort to prevent them from sending aid to gondor. all his forces were defeated except at the lonely mountain where the remnants of dale took up refuge in the mountain and prepared with dwarves to endure a long seige. but finally when saurons was defeated the host laying siege to the lonely mountain gave up and were routed from erebor. before the war there were dwarves in the iron mountains and ered luin (the blue mountains) and again in the lonely moutain.