Is there an efficient way to extract the juice from a fresh pomegranate?
Luckily you asked for an efficient way and not a clean way!
My brother in California has numerous mature pomegranate trees on his property and squeezes the majority of the fruit each year to use for jelly. He uses a manual Hamilton Beach Orange juicer which he says does the best job of anything he's tried. He usually has between 16-20 gallons of juice a year so he has definitely put it to the test. His local restaurant supply wanted around $250 for one but he got his on ebay for $150.
To minimize the mess he does it on an old table outside and covers himself with a large garbage bag by cutting a hole in the bottom for his head and the sides for his arms.
The easiest way I've come across is to separate the jewels, wrap them up in cheesecloth, and twist the cheesecloth slowly so that the juice is pressed out into a waiting bowl.