We discovered grilling with indirect heat several years ago, and it is a key method for several of our favorite recipes: our famous Lamb Tacos (Barbacoa de Borrego) and Grill-Roasted Chicken. Indirect heat cooks foods by reflected heat, much like roasting in an oven. Heat circulating inside the grill cooks the food more slowly and evenly than direct grilling, although you may turn the food partway through the cooking time to ensure uniform cooking and to distribute appetizing grill marks.
~We don't have a charcoal grill, so I can only pass on information about how to do it (below). I won't pretend to know enough about charcoal to answer any questions~
We have a gas grill, and indirect grilling is the easiest way to grill, especially if you are working with large roasts, whole chickens or legs of lamb, etc. Other than checking the temperature every half hour or so, once you put the meat on you're free to do other things.
For this cooking method, you will need a gas grill with at least two separate burners, a disposable aluminum foil pan for use as a drip pan, tongs, and an oven thermometer.
For indirect grilling with a gas grill: First, heat the grill using all the burners with the lid closed. This will effectively turn your grill into an oven. Turn off the burner directly beneath where the food will cook and put a drip pan on the fire grate. Place the food on the grill rack directly over the drip pan, and adjust the burners on either side of the food to equal amounts of heat.
Our grill has two separate burners, so we first turn on both burners to heat the grill. I turn the right burner off, place the drip pan over the right burner and the food over the drip pan. The left burner remains on, and the lid MUST remain closed. I use an oven thermometer, set on the rack next to the meat, to monitor the inside grill temperature, and adjust the flame on the left burner only as needed to maintain the appropriate temperature.
For indirect grilling with charcoal, this information comes directly from the Williams-Sonoma Complete Grilling Cookbook. To set up an indirect-heat fire in a charcoal grill, light your charcoal and place a drip pan on the fire grate and use long-handled tongs to position hot coals around the edge of the pan. Then put the food directly on the grill rack over the drip pan and cover the grill. For foods that require 40 minutes or more of cooking time, light a second batch of coals in another grill or other fireproof container and use them to replenish the fire as the first batch of coals dies out.