Of all the protein you can cook on a grill, I think fish is the most difficult. This is a technique I was taught at several restaurants when I work as a line cook. The fish that grills the best is a firm or dense type of fish like tuna, swordfish, or the many different types of bass. Salmon also is wonderful on the grill but takes a little more attention because the flesh is more delicate and has a high oil content.
First off, don't overcook the fish.
Start with a clean grill, you don't have to wash it clean. Just make sure the grates are wire brushed and free of any debris. It's easiest to do his when the grill is hot, I try to hit it right after I pull something off the grill before it gets baked on. But if you don't do that, not to worry just let your grill heat up.
Once you've wire brushed the grates take a wet cloth, be sure its cotton and wipe the grill down to remove any dust or carbon. Let the grill re-heat to high heat. Just before you place the fish on the grill, use another cloth to rub cooking oil over the grill and be generous with the oil on the cloth.
Season the fish with whatever you like and lightly coat with cooking oil and then place fish on the grill. I say place the fish because if you slap it down the flesh will get pushed down below the grates and make it harder for you to get your spatula underneath.
After 2-3 minutes gently work the spatula under the fish, lift and make a half-turn, place the fish back on the grill on the same side. This gives you the hash marks you see in the restaurants. In another 2-3 minutes your fish should be ready for the flip, again be gentle so as not to push the fish through the grill grates. If you can reduce the heat to medium-high or move the fish to a cooler part of the grill.
I can't say this enough, don't overcook your fish, you can always cook it more, but you can't uncook it. Fish is expensive, so you don't want to waste money if you're going to the effort to select fish for a meal. Remove the fish and try to serve immediately, the fish will keep cooking from the internal heat and start to lose moisture. I have included a recipe for maitre'd butter, or a simple lemon will brighten the flavor.
1 stick of butter soften
2 tbsp chopped fresh parsley
1 teaspoon lemon juice
pinch Kosher salt
Fresh ground pepper, a couple or 3 twists