You'll need a cutting board, knife, a big bowl filled with water, colander, and some paper towels.
Start off by finding the crown, the part of the fruit that looks like Jughead's hat. Trim off the top 1/2 inch. You will get a little juice spurting out on the cutting board. Turn the pomegranate around, and trim off the bottom 1/2 inch. You'll see parts of the aril pockets hidden inside the white pithy insides. Take the knife and score sections all around the fruit, going from top to bottom. Put the scored pomegranate in the bowl of water, and carefully start pulling the fruit apart, working underwater.
Here's my pom after I pulled it into two halves.
Working with a section at a time, take your fingers and work out the arils from the white part, again in the water bowl. You'll see the white pith float to the top and the arils will sink to the bottom. After you've freed all the arils, skim the top with a spoon or just pick out the stuff that's floating. Pour the water and arils into your colander to drain. Spread them out onto paper towels to dry a bit. Move them to a plastic container, topped with a paper towel and seal. Stash in the refrigerator, and these lil' rubies should last for 7-10 days.