Anybody who likes Thai cuisine likes lemon grass, as it is present in half the menu items of most restaurants from the soups and appetizers straight through the entrées. Many vernacular names are misleading, but lemon grass actually is a grass and it does smell and taste like lemons.
The genus Cymbopogon is distributed from southern Asia and its adjacent islands over into Africa. The source of most culinary lemongrass is C. citratus, which is grown in Southeast and South Asia (but is native to southern India and Sri Lanka). It is hardy and evergreen in USDA Zones 10 and 11, but the roots may survive and re-sprout to Zone 8. It is a clump grass and grows to be between 2 and 4 feet tall.
As a kitchen item it can be purchased both fresh and in powdered form. The fresh plants resemble scallions and are used in much the same way. If the plants are fresh enough, you can even put them in a vase and get them to root and then start your own patch of lemongrass. It prefers full sun. It is not only useful for culinary purposes, but it also quite attractive as an ornamental planting.
Citral, an essential oil, gives lemon grass its lemony scent and taste. It is a mixture of two terpenoids (geranial and neral) and has strong antimicrobial qualities and pheromonal effects in insects (it seems to attract bees, but repel other insects). These qualities give not only culinary but also medicinal purposes.
Cymbopogon nardus or citronella grass is grown as a source for citronella oil, which is used in soaps, candles, and insect-repellent sprays. It is thought to be native to Indonesia, but is grown widely in tropical Asia. It is used as a companion plant to tomatoes and broccoli because it wards of insects. It spreads vegetatively by its roots though, and can take over a garden unless confined in some way.
Lemon grass leaves and oil are both used as medicine for a variety of complaints, including anything to do with the digestive tract, aching joints, and headaches. None of these have been verified scientifically.
In addition to being used as a spice, lemon grass is also used to make tea in many cultures (Asian and in the tropical New World). While this tea is purported to be medicinal (e.g. reduces anxiety), that has not be verified.
But most people will be interested in growing it for use in the kitchen, and that is (if various websites can be believed) not that difficult. Not surprisingly, a plant that contains an oil that repels insects is not bothered by many pests, but it can succumb to spider mites when it is being kept indoors over the winter. The latter strategy is necessary in any area that experiences a frost. In a colder climate you can bring the plants indoors in the winter, trim them down to just a few inches tall, put them in small pots and stick them in a sunny window, keeping them barely moist to slow their growth.
In the warmer months you can put them in large (>12-inch diameter) pots or tubs. They can be harvested as soon as they get to be 12 inches tall. You can separate the plants you want from a clump, making sure to get the entire bulb at the bottom and even a few roots.
The heart of the bulb has the consistency of butter. This is the most flavorful part and is the best for cooking. (The leaves and the rest of the plant can be used to make teas and to flavor soups and stews.) You can mince or purée the inner part of the stalk base and freeze it, breaking off small pieces as needed.