Lemongrass (Cymbopogon citratus) plants are often sold in nurseries, but you can start your own with lemongrass bought at the grocery store. Trim the grassy ends to about 5 inches from the bulb end. Peel the outer layer from the bulb and place it in a glass of water. Keep the glass in a sunny windowsill indoors. Change the water weekly. Within several weeks, you will have well-rooted bulbs.
If it is not warm enough outdoors to plant vegetables such as tomatoes and peppers in your zone, pot your lemongrass bulbs 2 inches deep in potting soil and keep them indoors until the weather and soil are warm enough, after all danger of frost has passed.
Choose an area that receives a minimum of six hours of direct sunlight. Using a garden fork, dig up the soil and mix it half-and-half with rich compost, then smooth it out. Plant the bulbs 2 inches deep. Lemongrass will grow 3 to 6 feet tall in a season and the bulbs will multiply in moist, loose soil.
Lemongrass commonly grows in bogs or in steadily moist soil, so watering is critical. Water daily through the hot season. Mulch with straw, wood chips or compost to keep moisture levels even.
If you want to try overwintering lemongrass, plant it in a protected area, such as along a south-facing foundation or rock wall or in a fence corner. You could also plant it in a thick-walled ceramic pot and cover the whole pot with bubblewrap in the winter. Another option is to dig up a part of the plant before fall frost, pot it in potting soil and grow it inside. If you lack a sunny window, grow it 3 inches beneath fluorescent lights left on for 12 hours a day.