As far as I know, it's a tropical, so warm and humid conditions would be required.

Anne

I've seen Lemongrass growing wild (and very vigorously) in the Caribbean and it's usually considered a tropical plant, but it's actually border-line hardy in the UK, so, depending on where you are, you might be able to grow it in the garden in a very warm and sheltered spot. It's ideal in a heated greenhouse or conservatory too.

Otherwise It's very easily grown indoors. A sunny kitchen windowsill would suit it very well and allow you to crop the stems whenever you need them.

Incidentally, you can root Lemongrass from the fresh stems available in supermarkets. Just place the stems bulb downwards in a glass or jar or water, in as warm a spot as possible, and wait for them to develop roots. You can then pot the plants up into compost, being careful with the delicate new roots.

Ilex is right and the easiest way to start off your lemon grass is with a fresh stem from a supermarket. I didn't use the water method but just put them in pots of well drained moist compost and they rooted well, as the stems are pulled from the plant and some still have the basal roots attached.
They do very well in a greenhouse and I kept the plants alive for several years in an unheated polytunnel, until the very cold winters began a couple of years ago. I would grow them in the greenhouse border or a very large pot during the summer, when you should be able to harvest some from the clump, and then pot up enough to overwinter in a frost free place like a window sill or heated conservatory if you are lucky enough to have one.