Take a conical shaped part out of the bottom end of the fruit, as shown (avoiding cutting too deeply and breaking into the arils). The bottom is the crown looking end, away from where it was attached to the branch.
Score marks from the bottom to the top of the pomegranate so the fruit is marked into quarters, as in the photo.
Insert your thumbs into the opening at the bottom of the fruit, and gently pull apart. Do this over a bowl to catch any falling arils.
Break the pomegranate into halves, then into quarters.
Now gently remove the arils from the skin and pith, placing the fruit in a bowl and the discards in another.
Notes
Pomegranates can be eaten as is, or pressed for juice, to make cocktails, jelly and much more.