Break the ends off the asparagus by holding each stock upright and bending, it will break where it becomes tender enough to eat.
If you want your asparagus to be a bright green color, you should microwave them for 2-3 minutes on high and then plunge into an ice-water bath to cool them before grilling. Dry the stalks off before adding to the oil mixture.
Place the dry asparagus, olive oil, and thyme into a baggie and let sit for at least 30 minutes ( I usually make mine up hours ahead of time since its one less thing I will have to do when grilling and serving dinner.
Place the asparagus on the grill using either a grill pan or on the grate. If you place them directly, make sure you lay them perpendicular to the grate so they do not fall through. Rotate the asparagus every few minutes. Grill marks are good but do not burn or overcook.
The asparagus is cooked properly when you pick it up holding the stalk and it starts to slightly bend in the middle.