There are a few simple tips I live by when grilling fish.
First of all, it's easiest with "steak-like" fillets. Swordfish, Ahi tuna, Mahi Mahi, any of the thicker cuts are wonderful to grill.
Second, you'll want an oily marinade to avoid your fish sticking to the grates or in the very least, oiling the grill grates themselves to help with stickage prevention.
Third, you'll want to take care not to overcook your fillets. Fish is done when it's pierced with a fork & separates easily.
This fabulous recipe is a great one to start with. The flavor is fantastic and the Aioli gives just the right "punch" to it.
See for yourself, it's a cinch!

Aioli
1/2 cup mayonnaise
1 teaspoon prepared horseradish
2 or 3 dashes freshly ground black pepper
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1 pounds fish steaks, 3/4 to 1 inch thick
1/2 cup oil
1/3 cup low sodium soy sauce
2 tablespoons packed brown sugar
2 teaspoons sesame oil
2 teaspoons ground ginger
3 cloves garlic, finely chopped
In small bowl, mix all Aioli ingredients. Cover and refrigerate until serving.
If tuna steaks are large, cut into serving size pieces.
In shallow glass dish mix vegetable oil, soy sauce, brown sugar, sesame oil, ginger & garlic.
Add tuna & turn to coat with marinade. Cover dish and refrigerate for at least 2 hours but no longer than 4 hours.
Heat coals or gas grill.
Remove tuna from marinade; reserve marinade.
Cover and grill tuna about 4 inches from medium heat 10 to 15 minutes, brushing 2 to 3 times with marinade and turning once, until tuna flakes easily with fork.
Discard any remaining marinade. Serve hot with a dollop of Aioli on top.