The secret to cooking fish moist on the grill is two folds. Firstly, you want to make sure that your grill is hot and grill grates are cleaned and well-oiled. We want to make sure that fish cooks very fast, and if your grill is not clean and oiled, it will take longer and dry as a result. Secondly, you can use some of the marinades to brush the fish as it cooks, making sure that it is well-seasoned and moist.