Carefully pick out each pip (aril) with your fingers while holding the fruit underwater, carefully breaking the white membrane apart as you go. I try to use only my fingertips and not my nails at all, so I don’t puncture the pips and release any juice. You also might find that turning the skin inside out (carefully!) will release a lot the seeds without having to pick. Work slowly.
I love love love pomegranates. They are my favorite fruit by far and even if they are pricey, I like to get them at least once each year. The only drawback to the pomegranate is how messy it can be to get the pips (arils is the technical name) out of the skin. The juice will stain* clothing, cutting boards, tables, anything porous. I used to make such a mess that when I was in high school my mom banned me from peeling them in the house. That was before I figured out the underwater technique. There are many variations on this, some calling for you to remove the crown first, others call for you to quarter or even eighth the fruit, but I find this way to be the most efficient. Plus, the less you cut the fruit, the more whole pips you will end up with. Once you puncture the pip, the wonderful juice drains out, and you don’t want that!
I always buy the Pom Wonderful brand pomegranates (even though I think searching out branded fruit is a little odd) because they are always large and juicy. You want a large, heavy pomegranate with an unblemished skin. Pomegranate pips or arils can be frozen for up to a year, and the whole fruit will keep in your refrigerator for a couple of months. Pomegranates are full of antioxidants, and each one has exactly 840 seeds.
*it also turns bright blue when rubbed with Ivory soap, oddly enough.