Prickly pears are like the pineapples of the desert -- luscious tropical fruits with a thick rind that takes a little more than simple peeling to break through. If you buy prickly pears in the market, half the sticky work is taken care of; market-form pricklies have their annoying spines removed. To extract the rich, magenta nectar, you must steam or slice the rind away. If you choose the latter method, wear food-handler gloves in case you encounter an errant spine. Protect your work surface and clothes, too. Prickly pear juice stains, similar to beet juice.
Manually
Rinse the prickly pears and set them in a pot with about 1 inch of water. Bring the water to a simmer and cover; simmer the fruit for 10 minutes.
Drain the fruit in a colander and transfer them to a dry pot. Mash the fruit with a potato masher or fork.
Transfer the fruit to a large mesh strainer lined with two or three layers of cheesecloth set over a bowl. Drain the juice for several minutes them press the solids with a rubber spatula or the back of a spoon.
Squeeze the fruit solids in the cheesecloth and wring the juice from them. Discard the solids and store the juice in a glass airtight container in the refrigerator. You can use a plastic container, but expect it to stain.
Food Processor
Rinse the prickly pears and trim about 1/2 inch from the ends. Make a 1/2-inch-deep slice through the skin of the fruit, from top to bottom.
Grasp the skin where you made the incision and peel it off the fruit; it should come away in one piece.
Roughly chop the flesh and transfer it to a food processor. Puree the fruit until liquified, about 2 minutes on high.
Strain the juice through strainer lined with two or three layers of cheesecloth set over a bowl. Press on the fruit solids with the back of a spoon or rubber spatula. Transfer the juice to a glass storage container and store it in the refrigerator.