Summarize:

Use clean water, as you'll be consuming the pomegranate seeds. Add enough water to the bowl to cover both halves of the pomegranate. After it's been in the water for a few minutes, you'll start to see the white parts, called the pith, floating away from the pomegranate. As it does, the seeds will come out. Take out the skin, then skim off the white pith. Throw these in your compost or trash bin. Then, slowly pour the water and pomegranate seeds over a kitchen strainer. This will collect the seeds, which you can place in a bowl for use.
Fill a large bowl with fresh, cool water. Place the 2 halves in the water. Strain the pomegranate seeds into a bowl.