First, if you bought lemongrass from a market, you want to peel out the outer shell until you reach to the softer and white root. You won't see much greens left. That means it's good to use. If you take it out of your garden, you need to cut out the hard end first or it will be difficult to peel. Rinse and clean properly before chopping them.
The first step before using lemongrass in any dish. You want to cut the end bit. The hard end is chewy and you don't want them in your food. Cut the end out, usually about 1 cm from the root side.
The fist way to cut the lemongrass is to cut it diagonally, about 2 inches long. This one you can use in stir-fry dishes to add aroma. This style of chopping you can use 2/3 of the stalk from the root side.
Next style is to slice the lemongrass very very thin. Parallel to the width side. You can use this style in salad. Don't use the whole way. You can only use 1/3 of the stalk from the root side or the white side. The green side will be chewy.
Another style is to bruise the lemongrass. This will bring out the essential oil from the roots. It's good for Tom Yum soup and other kinds of soup. It's also great to use for making lemongrass tea. you can use 2/3 of the stalk for this style of preparation.
Lemon grass also use in may thai curries. Simply preparing the herbs the same way as mentioned above. Chopped them into smaller pieces before grind them in a mortar.