Preheat a grill.
Place asparagus on a plate. Drizzle oil over the asparagus and turn spears until they are coated. Sprinkle with salt and turn again.
Grill asparagus for 5 minutes over a hot grill. Each minute or so, roll each spear 1/4 turn. Asparagus should begin to brown in spots (indicating that the natural sugars are caramelizing) but should it not be allowed to char. Dripping oil may cause flare-ups. Keep a glass, or spray bottle of water handy to spritz on coals, if necessary.
Remove from grill and serve immediately (eating spears with your fingers enhances the experience).
Look for firm asparagus stalks with firm deep green or purplish tips. Also check the bottom of the spears. If they are dried up, chances are they have been sitting around for too long. Trim off the tough bottom of the spear by grasping each end and bending it gently until it snaps at its natural point of tenderness, usually 2/3 of the way down the spear. If the spear is less than 6 inches long, chances are it has already been trimmed for you. Then take a vegetable peeler and peel off the outer skin of the lower half of the remaining stalk.