Slice the top half inch of the pomegranate off (this is where you may cut through a couple of arils. I don't sweat it, but if you prefer not to, you can cut a little less off, and it just requires a little more hand strength when separating the sections.)
Find where the white membranes separate the sections (they're found along the ridges that you can see on the skin). There are usually 5-7.
With a paring knife, carefully score the flesh from the top to the bottom along each membrane.
Over a bowl or dish, pry the sections apart in your hands and remove any membranes.
Carefully push and flex the skin of each section so the arils begin to pop out. Remove any other seeds with your hands.
Video
Notes
To store pomegranate arils: Transfer the pomegranate seeds to an airtight container or baggie and store in the refrigerator for 4-5 days. To freeze pomegranate arils: Lay the pomegranate seeds on a parchment lined baking sheet in a single layer. Freeze for 1 hour. Remove the baking sheet and transfer the partially frozen pomegranate seeds to an airtight container or freezer safe plastic bag, squeezing out as much air as possible as you close it. Return to the freezer for 3-4 months.