Trim the asparagus (see Note). Toss the asparagus spears with the oil in a shallow platter of rimmed baking sheet. Sprinkle with salt.
Grill the asparagus with the spears perpendicular to the grate, or in a grill basket, 4 to 8 minutes, depending on thickness, and how tender you like them to be (see additional tips above). Turn them every minute or two. Don’t forget they will get a bit softer once they are removed from the heat, so take them off just before they are done to your liking. Keep checking, turning, and moving them around as needed. Remove from the grill and serve warm or at room temperature.
Notes
Trimming Asparagus for GrillingA common method for removing the woodier bottoms with their thick skins from asparagus stalks is to hold the stalk in the middle and by the bottom end and to bend it until it snaps, removing the fibrous bottom few inches from the stalk. I hate tossing some of a perfectly good stalk of asparagus, so I like to cut off in inch or so from the bottom and then, for thick asparagus, peel the bottoms of the stalks to remove the tough outer skin of the spear, going about 3-inch up from the bottom of the stalk. Use a vegetable peeler for this task.For thin asparagus, you can just cut the bottom inch or so off the asparagus.