Cut a circle around the top of the pomegranate using a sharp paring knife (the top looks like a crown).
Make shallow cuts along the ridges of the pomegranate, around 5 - 6 cuts. After you make the cuts, use your hands to open the fruit and gently divide it into segments.
Submerge the pomegranate in the bowl with water, and use your hands to gently remove the seeds from the skin and membranes while still under water.
The seeds will sink to the bottom of the bowl, while the white, spongy membranes will float to the top. Skim off the white bits, and drain the seeds.
Notes
Pomegranate juice stains everything, it is best to remove the pomegranate arils in a bowl with water to prevent from juice spraying everywhere.
Make sure you cut along the gentle ridges on the outside of the pomegranate, just through the red part of the pomegranate skin. You can feel the ridges with your fingers or look for a slight dent on the skin.