Upward Facing Dog and Downward Facing Dog are counterposes of one another, so they are related in the context of yoga. However, these positions are actually quite different.  While Upward Facing Dog is a prone pose (meaning you are belly down), Downward Facing Dog is an arm balance that involves balancing on your hands and feet while pointing your hips upward towards the sky.  Whereas Upward Facing Dog requires you to support your weight on the tops of your feet as well as your arms, in Downward Facing Dog, you will be balancing your weight on the soles of your feet.  In Upward Facing Dog, your arms should come straight down with your hands on the mat underneath your shoulders. In Downward Facing Dog, your hands come forward past your head, and rather than being lifted, your head hangs down toward the mat. Your body basically forms a triangle shape with your hips pointed to the sky.  You can easily transition from Upward Facing Down to Downward Facing Dog by curling your toes under and pressing up through plank, lifting your hips, and bringing your heels down toward the mat. To return to Upward Facing Dog from Downward Facing Dog, return to a plank pose and lower to Chaturanga before pressing up through the palms of your hands.