Collecting the Fruit:
First you need to collect the fruit. There are many varieties of prickly pear cactus, and as far as I know, both the fruit and pads are edible on all Western North American Opuntia species. These are the flat, beaver-tail shaped cactus. Not all of them produce a good fruit for eating though-I have a beautiful purple prickly pear in front of my house, but the fruit are too shriveled and dry to use. You want to find some that are a deep purple-red in color, and are nice and plump (there are some varieties where the fruit is ripe when yellow or green, though none of these seem to grow wild in my area, so I am unfamiliar with them, or how well their fruit works for jelly). The flesh should be firm, if the fruit dents without much pressure from you, it is probably getting too ripe to use. The fruit is sweet and edible without cooking-but between the thorns and seeds, I prefer to juice it.
You can collect the fruit from public lands-usually a small amount for personal use is permitted-though if you plan on selling the fruit or products (like jelly) check the regulations. If collecting on private land, please get permission, and make sure no pesticides or herbicides have been used near the plant. The time of year the fruit will be ready depends on the weather, the species and your location, but is usually ripe in late July through September.
Yes, you can use gloves-but trust me, you'll get poked anyway, and you'll end up having to toss the gloves because the glochids get stuck in the gloves, and end up getting in you whenever you use them after that. I've found the easiest way to get the fruit is to use some kitchen tongs. They keep your hands out of the way of both the big spines and the glochids. I suggest you put the fruit in a plastic bucket to further contain the spines. If it's a bucket you want to use again, you'll need to hose it out, then use something abrasive to get rid of all the spines. A better idea is to ask your bakery if they have any buckets they are going to toss, some of their frosting and dough comes in buckets. I've even picked up some at Dairy Queen before. Then you can just recycle the bucket when you are done.
(A few tricks: put a bottle in a drawer next to the stove to catch drips, and so you don't have to handle a hot jar of juice. Another trick is to put a few marbles in the water pan-they will start to rattle when the water level gets too low, so you can avoid boiling the pan dry-which is bad...Very bad.)
If you don't have a juicer, place the fruits whole into a pot, bring to a boil, and boil for ten minutes. Mash with a potato masher, then boil for another ten minutes. Pour juice out through cheesecloth to strain.
Once you have the juice you can make jelly immediately, or you can freeze the juice to make it later. Find a recipe from a reliable source such as a university extension office or official canning website like Ball or Kerr. Jelly is a little safer to experiment with than other canning foods, but you don't want to risk wasting your work on something that is potentially dangerous to eat. Recipes from these sources have been tested for safety.
It always helps if the little ones don't get tired of you cooking and try to push you out of the kitchen.
This recipe is from Preserving Food in Wyoming: Wild Berries and Other Wild Fruit by the University of Wyoming Cooperative Extension Service, College of Agriculture and Natural Resources, p. 23. You can find the entire publication here.
Prickly Pear Jelly
3 cups of cactus juice (made from approximately 12 cups ripe cactus fruit)
½ cup lemon juice
1 package of powdered pectin
4½ cups of sugar
Jelly bag or three layers of cheesecloth
Mix cactus juice and lemon juice with powdered pectin. Place over high heat and stir until the mixture comes to a rolling boil. Add sugar, bring to a vigorous boil again, and boil for 1½ minutes stirring constantly. Remove from heat, skim off any foam, and pour quickly into hot half-pint or pint jars or hot sterilized half-pint or pint jars leaving ¼-inch headspace. Wipe sealing edge of jars with a clean, damp paper towel. Adjust lids and process in a boiling-water canner, for 10 minutes, adjusting processing time for altitude. For good instructions on using the water bath canning method, and a chart for adjusting processing times, go here.