I invested in a hand-crank citrus juicer and it's the best I've ever used--faster and easier to use. You can juice a pomagranate same way as an orange. First, cut it in half:
Then put it in the juicer and smash with the crank:
I also tried some concord grapes for fun:
It was a little more messy. I tasted this and it was yummy. I added the rest to a smoothie. mmmm.