The best way to grill shrimp is on skewers, on an oiled grill rack.
First, soak 12-inch long skewers in water for a least 30 minutes.
Preheat grill to high.
Put vegetable oil or olive oil in a small bowl. Soak an old dishcloth or paper towel in the oil, draining off excess. When the grill is hot, using grill tongs, carefully run the oil-soaked cloth quickly over the grill surface to coat. It may flame up a bit, but that’s OK, it should stop quickly.
Thread shelled shrimp on skewers, piercing through the head and the tail of each shrimp so they form a “u” on the skewer. Place skewered shrimp on the oiled surface and grill, uncovered.
When the shrimp no longer stick to the grill surface, they are ready to flip over and continue cooking, just until pink (usually around 2 to 4 minutes per side).