I stuck the base in some water, and just a couple days later there was quite a bit of growth.
About a week later I put it in a pot with soil up to the top of the original base. Now it's really taking off! I'm looking forward to having a couple small stalks ready at a time. Really that's all I use at once, so it's hard to use up a whole entire bunch of it.
Plus it's a pretty plant :)