The problem, I think, is that terms are not always specified. What ONE? What TWO?
Generally the reading is like this:
One is Wuji, the unified force of yin and yang. Wuji in form represents stillness, because yin and yang are indistinguishable.
Two is Taiji, yin and yang as distinct but INTERDEPENDENT forces, in constant motion.
Three is variously San Cai (the Three Powers), or yin, yang and stillness. In the latter, the interaction between these three things causes everything else to happen. In the former, the Three Powers are Heaven (Tian - yang), Earth (Di - yin) and Humanity (Ren - balancing the two).
Dao is what causes all of this to happen. The closest analogy I can find is the Force in Star Wars. It is the energy that binds the universe together, causes all things to be connected to all other things, and directs all motion in the course of natural action. That "Dao begot the one" means that the original formation of the natural universe was created by Dao in the state of oneness: Wuji.
I hope this helps