The "true" dragon tree, Dracaena draco? The indoor houseplant version Dracaena marginata? 'Flying Dragon' Poncirus?

Actually, though, when I think about it, it doesn't matter that much -- any of the above can be propagated by tip cuttings, stem cuttings, and seeds (if you can get them).

Is it getting to tall and leggy? What exactly do you want to do with it?

I got one for a friend, and she now has ten of them. All she did was cut the top off and stick it in a pot, then let the original stem sprout. It seems to be really easy and most all of the cuttings have survived and thrived.

I thought this was interesting to see what happens when you cut the top off of one...

one of these plants spontaneously sprout like that in the video. I'm sad to say the remaining three are very thin. I would like to cut them off and give the stock a chance to regrow. I was hoping that I wouldn't have to cover it up. Looks like it should work just fine.

The common indoor houseplant.

You can cut off the green tops and root those. You can also cut the canes into pieces of virtually any size from 2" long on up and root those.

The cuttings should root in water or soil. Be sure to let them sit out on the counter for about 24 hours to callous the cut ends before you try to root them.

I understand about the cane, but should the green tops sit out also for 24 hours?

It won't hurt them a bit. The leaves might get slightly droopy. You should probably pull a few of the bottom ones off, anyway, since they would just rot in the soil or water.

I'd also suggest using a rooting hormone powder (sold at most any garden center) if you try rooting them in soil

The callousing process that the cut wound will undergo as it sits exposed to the air is important - -the plant starts making corky tissue which repels disease organisms.

Dracaena marginata is a tough plant, you should find it easy to root. Be patient, though, it can take a couple of months for the cane sections to start showing any development.