Propagating Bougainvillea

Tweet

I have a medium-ish, flowering bougainvillea in a plastic bucket. I want to transplant it into a larger pot to give it more room to branch out and I'd like to be able to propagate some cuttings from it to make some small hanging baskets. Problem is... I don't know how to propagate bougainvillea... or even if it is possible to do it. I've looked on the web, but don't really see anything of any help. Has anyone ever done this? How would I go about it?