How should I cook a full rack of ribs on the grill?

As slow as possible. Check out http://www.foodnetwork.com/food/recipes/recipe/0,,FOOD_9936_11125,00.html?rsrc=search

Who recommends not doing them on the grill -- it's really hard to regulate temperature, and they're just as tasty not. If you really want that grilled flavor, cook them in the oven, then transfer to a medium-to-high heat grill, and finish them there for about a minute or two.

Smoking them over many hours is probably the best route, but you need a smoker, not a grill. In addition to baking, then finishing on the grill. You can boil, then finish on the grill. Sauce when they are about finished, otherwise it will burn on the ribs.

First I sear them on the grill. Then I mix a 12 ounce jar of B-B-Que sauce with an equal amount of water, 4 ounces of bourbon add seasoning like caynne pepper to your taste level. Boil your ribs in this mixture covered (I get a throw away tin pan and cover it with foil) on the grill for a few hours. The ribs will be soooo tender you may be able to eat the bones!