It moves from the oviduct to the uterus by the help of cilia and the contraction of muscles in the oviduct (peristalsis).
Cilia are like little hair, they sway and they can be able to move things towards another direction. Cilia are not only present in oviduct to move eggs, but also in many other locations in our body such as in the trachea, to move mucus away.
And peristalsis is the contraction of muscles. The muscles behind the egg squeezes, the muscles in front of the egg relaxes, and pushes the egg towards the uterus. Just like cilia, this movement can also be applied to other location in body, such as moving food bolus towards the stomach.
Together they're able to move the fertilized eggs (or even unfertilized ones) to the uterus for a place for development.
