Use moderate heat so you don't burn the fruit. When using gas, I grill fruit with the lid down to take advantage of ambient heat, but I also keep the temperature to medium-too high and the hot grates will burn all that natural sugar in the fruit.
Because fruit is delicate, I move it around as little as possible. I use tongs and usually find that they are adequate for turning and removing fruit from the grill. For a little extra help, I hold the back of the fruit in place with a pair of tongs and slide a spatula under the fruit to flip gently. I like a silicone spatula with a deep off-set neck so you don't have to dig under the food, just simply slide and lift. If the marinade or rub causes the edges to stick or they've burned a bit, I gently loosen with the edge of a tong or spatula before turning or removing from the grill.
Serve when you like. One of the best things about grilling fruit is that it never needs to be served piping hot. In fact, many fruits are better once they have cooled to room temperature, so you can grill the fruit in advance. If you do want the fruit to be piping hot, plan on about 10 minutes to grill the fruit and serve it. If you're serving it over ice cream, be sure to let it rest a few minutes or it will melt the ice cream faster than you can serve it.