You can remove the white pith and seeds from the oranges. To remove the pomegranate, cut open the fruit and remove the seeds; another way is to peel off the skin (you can buy pre-seeded pomegranates to save time).
Using a Blender
Add the oranges and pomegranate to a blender with water just enough to cover them, and blend.
Transfer to a squeeze cloth or fine mesh cloth, squeeze out all the juice, and serve.
Using a Juicer
Turn on the juicer and put the fruits in the feeding tube.
Collect the juice and pulp in separate containers. Pour into a glass and serve.