Use tongs and gloves to pick and wash, then simmer the fruit with a little water, piercing or cutting it open as it heats up, to let the juice out, you can avoid the spines. Mash it up a little with a potato masher or what-ever, then use a jelly bag, or 6 gallon paint strainer to separate the pieces from the juice, like making jelly. Before you pick it, be sure the fruit is almost black, and almost falls off the plant when you grip it with the tongs, if it is like the ones I saw in the beginning of this post. The ones in the picture looked less ripe than I pick them.
I talked to a farmer at a farmer's market that was handling his "tunas" (prickly pear fruit) with his hands, and after extensive questioning, he said he puts them in a sand pit and brushes the sand over them with a broom till he gets all the stickers off. I haven't tried that yet. I expect you would have to be really careful of the sand, it would be full of stickers.