Far and away the easiest thing is to pot up a well-rooted sucker, or bend a branch over and air-layer it for a year(ish) to "make" a sucker to take off.
You can do it from greenwood cuttings but it's a lot more work and lower success rate. You have to catch things at the right stage of growth to have best chance of success.
If you're wanting to propagate from the cut-down bush you may not have a lot of luck but what the heck, you can try... cut off like 6" of new growth, strip off all but the top 2-3 leaves, dip in rooting hormone powder, and pot up in low-nutrient seed starting medium and keep brightly lit BUT NO SUNLIGHT and evenly moist, with a plastic bag mostly over it (not tightly sealed). I'd start a bunch of them, in hopes that one will strike. When you see new growth, it means some roots have probably formed and you can start pulling the plastic bag off a little at a time to get it used to normal humidity. It will take a lot of growing-on and hardening-off, I wouldn't contemplate putting it in the ground for real until next year.