Italian style: Snap off the woody part. Toss with some olive oil, balsamic, minced garlic, salt, and pepper. Grill until you see a few black spots, and serve. You can also put them on a grill pan in a very hot oven.
Austrian style: Take white asparagus, cut off the woody ends, trim the outside of the stalk. Steam or boil until tender, then drain, toss with butter, salt and pepper to taste, then drizzle with a little bit of roasted pumpkinseed oil (Kurbiskernoel).