Opuntia are actually extremely easy to root (aside with my issues with trying to root store bought pads). Just use either a pair of pruning shears or scissors to remove the pads. Each pad will grow a new plant. You can remove solitary pads or several attached, it's up to you. Place the pad(s) perpendicular to the surface of some well-draining soil, do NOT water it. I will use rocks some tiimes just to support the pads until they root. The soil should be only slightly moist to the touch..., you don't want it to rot. Should root.

This one is the Eastern Prickly Pear that flowers in June.

Thanks very much for your post @Jurassic Park. ..I learned lots.