Use a sharp knife to cut the top of the pomegranate, about 1/4 inch.
Score the sides of the pomegranate. Holding the fruit, you might notice that there are 5-6 gentle ridges in its surface. Use your knife to make thin slits along those ridges. You should be cutting along the fruit's white pith, not slicing open any of the arils. After you make the cuts, use your hands to peel the fruit open and gently divide it into segments.
Fill a large bowl with water. Submerge the segments, and use your hands to remove the seeds from the skin and membranes.
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.