I get a lot of requests for information on how to grill fish properly. The first rule I've found is not to think about it too much. Fish is meant to be grilled. The direct heat cooks fish fast, easy and without removing moisture. Grilled fish is quite flavorful and juicy. The second rule about grilling fish is to make sure it doesn't stick. Whether you oil the cooking surface or brush the fish with a little oil, make sure that you have a non-stick surface to work with.
Apart from that, grilling fish is easy and fast. You can literally get fish off the grill in a matter of minutes, thus making fish the perfect after work meal. Pick up a couple of fillets and lemon or two and light up the grill as soon as you get home. Fish is also great for dinner parties when you have a steady stream of guest trickling in. Before dinner, you can get the fish soaking in a marinade (or otherwise seasoned up) and light up the grill a few minutes before everyone wants to eat.
The hardest part of grilling fish is knowing when it's done. This is generally the trickiest part of grilling, but don't worry. When fish is cooked the meat will flake easily with a fork and will appear opaque all the way through. If any part of the meat is still glossy and partially translucent then it's not done. Don't ever serve undercooked fish. Not only is it unsafe, but you might turn someone off fish for life.
To make this easy, always start out with a steak or fillet that is evenly cut. If one part is much thicker than another it will be hard getting the thick part cooked before the thin part dries out. If you have a fillet that is uneven consider cutting it in two. Put the thick half on first and when it's about halfway done, put the thin half on.
This way you will get the fish cooked to perfection without burning anything.
Generally, you buy fish either whole or in fillets or steaks. Fillets will give you the most trouble because they tend to fall apart a little easier. This takes us back to the two rules. With an oiled surface (use a high smoke point oil) put the fish on the grill and leave it until you are ready to flip. Flip gently and leave it there until it is ready to be taken off the grill. With fillets, you can tell it is ready to flip because the edges are flaky and opaque. Do not attempt to grill large fillets, but instead, cut them into smaller pieces that will be easier to handle. Steaks and whole fish hold together better but take longer to grill. If you are grilling whole fish stuff it with something like lemon slices and herbs. This not only adds to the flavor but creates a space inside the fish to let the heat cook through more evenly.
Also, keep some fresh lemon juice and maybe some melted butter handy while you are grilling.
You can brush this on as you grill to add flavor and keep the fish moist. But remember that butter will burn so be careful with it. I love dripping lemon juice over fish while I grill it. The steam and the sizzle add to the show and makes everyone appreciate the meal just a little bit more.