I got me a pad by the side of the road. Laid that sucker flat in a 6-inch shallow plastic pot filled with good-draining soil, put a rock on it so that squirrels couldn't disturb it and just left it alone outside in semi-shaded conditions. It has puffed up and has a new growth on it. I think they'll root anywhere the pad touches soil. Rooting hormone? Might help if you've cut the pad. I think I got my pad last Winter. My method of rooting is probably not the fastest or best, but it worked, which means these things are fool-proof pretty much.
Hope you got varieties with mellow spines.

I rooted mine easily, just stuck it in the dirt.

If you feel safer using Rooting Hormone, then sprinkle or dip RH on the side leaf will be inserted in soil.
I stick pads in soil, place in a medium light, and wait..

Your Optunia engelmannii has HUGE thorns..Be careful when handling. Toni

I found out about the thorns the hard way lol suckers are kinda small actually, but a pain to get out like little slivers. Do you guys stick it upright, or is laying it flat better?

There's some prickly pears growing on campus here in a tiny praeries garden on campus. They're calling them O. Humifusa, but they don't look like that, and I'm questioning whether they're cold hardy. Anyway, they tend to rot in the winter because they're not really planted right so I'm considering asking whoever manages the garden if I can take a cutting. Assuming I can get permission, what's the best way of doing this? Do the pads break off from eachother fairly easy? Would I need some sort of cutting tool?

When pruning the giant Opuntia in my apartment's back yard, I use a sharp kitchen knife and a rubber mallet. Line the knife up where you want to make the cut, then strike it with the rubber mallet. Fast, clean cuts...

For smaller plants, the mallet is probably over kill.

No hormone needed. They have plenty of their own. They're similar to a Willow tree, in that as long as the part is still alive when you plant it, it will root.

I planted mine 'vertically' but it tips over a lot. So it might work better if you tip it over and put about 1/2 the pad in the soil. Both the new pads and the new roots will grow out of where the spines are.

I root pad, standing upright..too afraid leaf will rot if it's lying horizontally. Doesn't Optunia root where it was cut?

Is there a way to tell a hardy Optunia, (hardy meaning, survives in 5-10F temps) from non-hardy?
Also, do hardy Optunias, when mature, flower/fruit?
We planted Optunia in the garden several yrs ago. It grew wide, not tall. Is there a hardy, tall type? Thanks, Toni

PS..yep, gotta handle Optunia with caution..Tiny thorns are worse than large..they stick in your hand, are almost impossible eyeing let alone getting out. If you grab a pad, your hand will be clustered-filled-thorns. :(

I'll be happy to answer that question for you hopefulauthor since I grow and sell the cuttings and seeds and care for them on a daily basis. A Prickly Pear cutting will root from any side touching soil but it's best to plant the wound in the ground since it's already focusing on the part of it. Prickly Pears or Optunias are extremely hardy and are able to live anywhere from Mexico to parts of Canada but as long as they're properly watched and cared for when temps fall to drastic levels. Cold Wind, Frost, and snow will damage the plants but the plants are so hardy 9/10 they come right back once the temp goes up some or they are being kept warm and protected. I suggest getting a cutting that has been grown and cared for in temps and weather similar to yours to make things a lot easier for you in the beginning. If you live in zone 8 like myself, it would basically be a just plant it and forget ordeal and would require little to no watering since once the cacti establish their roots they can survive off adequate rainfall alone. A cutting and/or plant as it grows will bloom and flower and show new growth but in order to get fruit the plant has to be up to around 10 lbs but I've been able to produce fruit off a cutting about a month after rooting it but it's never guaranteed. On growing the cacti tall, that requires trimming and ties and pvc pipes or anything heavy enough to hold the plant in place as it grows in the way you are trying to manipulate it too. The attached picture is a cutting I sold 2 weeks ago to a guy in Virginia and he sent me back a update pic of the growth and says it is growing by the day as if it was a weed.