Pulse the seeds a few times until they break apart and release their juice.
Using a mesh strainer, strain pomegranate liquid into a bowl.
Use the back of a spoon to gently push against the pomegranate pulp and extract as much juice as possible. The pomegranate pulp should be relatively dry when you have extracted all the juice.
Chill and serve cold.
Notes
If using a fresh pomegranate, make sure that it is ripe for the best flavor. It should be heavy for it's size and firm to the touch.
I used a high speed blender, but a medium speed blender will do the job well.
Use a double mesh strainer if you have one to decrease the amount of pulp in the juice.