There are two theories most widely accepted as to where dot painting originated.
One, is that many of the Aboriginal men who began painting commercially during the Papunya Art Movement in the 1970's were concerned that non initiates may be able to understand or learn the sacred, secret or restricted parts of their stories. Acrylic painting brought a permanence to these symbols which had in the past been drawn in the sand and smoothed away after the ceremony or story was told. Or they were painted or etched onto sacred sites which were only visited by appropriate tribes people. This caused much discourse among tribes at Papunya, and dots began appearing on paintings thereafter, generally superimposed over the top of the sacred symbols creating a 'veil' hiding what was not to be seen.
The second, which perhaps works in harmony with above, is that drawing symbols in the sand already had a natural dotting effect, and so dots that appeared in the paintings reflected that speckle of sand and gave the paintings and symbols a truer essence.
This is not to say dots are new to Aboriginal art and culture however. Ceremonial body paint designs belonging to some groups have incorporated dots for generations, if not far longer.
The practice of dot work being applied over symbols in paintings has largely become redundant, as it is widely understood that the uninitiated westerner cannot understand the iconography anyway, and often very sacred symbols and stories are kept strictly within the culture.
Dots are generally applied with one of two instruments. One, bamboo satay sticks. The larger flat end is more commonly used for single application of dots to paintings, but the sharp pointy end can be painstakingly used to create even finer dots as well. To create superimposed dotting, artists will often take a bunch of satay sticks, dip the pointy ends into the paint and then transfer it onto the canvas in quick successions of dotting. This technique is often seen in Kathleen Kemarre's Bush Medicine paintings. The second instrument is ink bottles which are filled up with acrylic paint and squeezed out through different sized nibs. This technique, while somewhat quicker, still takes some time to master so that the paint does not squirt or run out all at once - ruining what might have been a very involved artwork.