Lemongrass is a grass grown in tropical climates, notably in Southeast Asia.  A common ingredient in many local dishes, lemongrass provides a zesty lemon flavor and aroma.
The best way to take the 'mystery' out of cooking with lemongrass is to understand how to purchase and prepare it:
When purchasing lemongrass, look for firm stalks.  The lower part of the stalk should be pale yellow, while the upper part of the stalk is green.  Lemongrass can be found in many grocery stores or in Asian markets in the produce section or freezer aisle. 

Preparing fresh lemongrass:

Cut off the lower bulb and remove tough, outer leaves.  The main stalk, the pale yellow section, is the part used in most recipes.  The stalk can be prepared in two ways:

  1. Cut the stalk into 2-3 inch lengths.  Then bend these sections several times and add them to your recipe.  Before serving, be sure to remove the lemongrass pieces from the dish.
  2. Cut the stalk into thin slices and place them in a food processor.  Add the lemongrass to your recipe. Lemongrass prepared this way can remain in the dish when served.

Ready-to-use lemongrass can also be purchased in the freezer aisle of your local grocery store or Asian market.

Source: http://thaifood.about.com/od/thaicookingessentials/a/Lemongrass.htm