There are a few steps you need to take before you get to the actual grilling of the shrimp. First, you'll have to peel them. Peeling shrimp consists of gently pulling the legs off the shells. Next, you'll want to use your fingers in order to loosen the shells; the shells should slide right off this way. The next step is to de-vein the shrimp. You can do this with the help of a sharp paring knife, which you will use to make a slit in the shrimp's back and to remove the vein. You may find that this is easier to do if it's done under running water.
Having prepared your shrimp for cooking, you'll now want to get your barbecue grill ready for use – clean it and fire it up. Once you've done so, break out the all-important grilling basket. The reason that a grilling basket is such a handy cooking tool to have is that it makes turning the shrimp much easier. Furthermore, the grilling basket will prevent the shrimp from getting stuck to the grill or falling through the grates. You also have the option of taking the shrimp and threading them onto skewers. You'll then want to place either the skewers or the basket on the preheated grill.
When you cook up a batch of shrimp, keep the grill uncovered and use a medium heat (one layer of coals or a medium flame on a gas grill). As far as time is concerned, it should take between six and eight minutes for your shrimp to cook through. Another way to know when your shrimp are ready is by checking the color; once the shrimp have turned opaque, they're good and ready. Don't forget to turn the shrimp about midway through the grilling time.