The language was created by the Vala Aulë, the creator of the first Dwarves, who taught them "the language he had devised for them," implying that Khuzdul is a constructed language even within context of the books. The language was rarely heard by outsiders and was a secret. The Dark Elf Eöl, who was a great friend and confidant of the Dwarves may have been verse in it as he regularly met with the Dwarves in the their ancient cities in the Blue Mountains during the First Age, but this is not recorded. Only one saying entered recorded history, the battle-cry, "Baruk Khazâd! Khazâd ai-mênu!", meaning, "Axes of the Dwarves! The Dwarves are upon you!".
According to the Lhammas, Khuzdul is unique in belonging to a separate language phylum, Aulëan, not related to the languages of Elves, which are in the Oromëan language phylum. Aulëan was named from the Dwarvish tradition that it had been devised by Aulë the Smith, the Vala who created the Dwarves.
There are many similarities between Khuzdul and the native tongues of men, such as Taliska, the language of the first and third houses of the Edain. This is because in the early days of Middle-earth, before men crossed the mountains into Beleriand, they had contact with the Dwarves of the Blue Mountains and further East. Taliska was the ancestor of Adûnaic, the tongue of Númenor, and the direct ancestor of the Common Speech, and both languages still had Khuzdul influences.
Instead of 26, Khuzdul has 50 letters in its alphabet which are more like sounds than actual letters.
Behind the scenes
The Dwarvish language sounds much like Hebrew, and indeed Tolkien noted some similarities between Dwarves and Jews: both were "at once natives and aliens in their habitations, speaking the languages of the country, but with an accent due to their own private tongue" (Letters, 176). Another reason Hebrew was chosen as a basis for Khuzdul is that it is unlike any of the European languages, and thus sufficiently alien to western ears to show just how different the Dwarven speech was from the Elvish languages. Although Dwarven symbols are identical to those of Nordic Runes, the symbols that correlate to specific English letters have been mixed around and even a few Runes have been inverted.
For the The Lord of the Rings movie trilogy, the linguist David Salo used what little is known of Khuzdul to create a semi-complete language for use in the movies. This is usually referred to as neo-Khuzdul by Tolkienists, which is a fully usable language. In addition, there is a website known as the Dwarrow Scholar which has released a complete, fan-made dictionary of Neo-Khuzdul.