They were made by Aulė, the smith and craft master of the Valar. This was against Eru's Plan: Aulė had neither the authority nor indeed the power to create other souls (the result of his efforts was a group of what amounted to puppets). However, because he repented his folly at once and because his motives had been good (he desired children to teach, not slaves to command) Eru gave the Dwarves life and made them part of the Plan. The Elves were still to be the "Firstborn", though, so the Dwarves had to sleep until after the Elves awoke.
Since beards were part of the appearance, not the garb, of dwarf-men, we must conclude that dwarf-women did in fact have beards. The question has been raised as to whether all dwarf men necessarily had beards (the above conclusion depends upon this premise). Insofar as the matter was mentioned at all, it was shown through either direct statements or casual references that at least Thorin, Dwalin, Balin, Fili, Kili, Gloin, Bombur, and Gimli all definitely had beards it is natural to assume that the others did as well. While no definite statement about the beard status of dwarf-men in general was ever presented as a matter of lore. In any event, the notion of bearded dwarves seems an assumption with fairly firm foundations.
Excited To See You Come In, Happy To See You Stay, Sorry To Hear You're Leaving, Devastated To Know You're Gone.
