Indirect and direct cooking methods work best when you can cover the fire and the food to contain the heat. A grill/smoker, for example, with a lid works best for this.
Cooking your food directly over hot coals or flame is the direct method of cooking while offsetting the coals so they are not under the food is the indirect method.
Direct Cooking Method
Smaller cuts of meats and vegetables that require very short cooking times would normally be cooked using the direct method. Steaks, chops, quartered onions, tomatoes, chicken legs, and thighs and breasts are just some examples of foods you would usually cook directly over the heat.
You want to sear the foods quickly to seal in the juices, you want the color (grill marks for example) and, of course, you want the flavor. Searing produces a caramelized texture that adds flavor to the food, as well as, sealing in the juices.
Build your bed of coals using charcoal or wood chunks 30 minutes or so before, you are ready to put the food on. You want the charcoal to be gray/ash colored, and you need enough coals to maintain a constant heat. When using all wood you may have more flare ups unless you let the wood turn into charcoal, and this can take longer, so plan accordingly.
Flames are okay to sear the foods, but if you let the flames get out of hand you may end up with a charred outside and an undercooked inside. A small spray bottle of water can be used to control flare-ups.
To keep foods from sticking to the grates allow the grates to heat up before putting the food on, and once you do lay that nice juicy steak on the grill leave it alone for a few minutes. The natural juices along with the searing process will allow you to turn the steak without it sticking, but it needs to be left alone for the process to work.
People tend to want to poke and prod and generally fiddle with food once on the grill. Put the food on, cover if you want to and let it cook a few minutes before turning.
Bring your foods up to room temperature by setting out for 20-30 minutes before putting on the grill, because cold foods put directly over heat will not always cook evenly, you again will end up with a charred outside and a cold middle.
Indirect Cooking Method
There are several ways of cooking using the indirect method. One method is to put the bed of coals on one side of the grill and then place the food on the other side of the grill. The second method would be to split the coal bed evenly and then place a bed of coals on each side of the grill leaving a space in the middle for the food.
Some believe that by splitting the coals beds with the food in the middle you get more uniform cooking. However, if you have a good cover and an adequately sized coal bed you certainly should not have any trouble with even cooking regardless of how the coals are situated. The hot air will rise and strike the cover and flow back down and around the food, regardless of where the coals are placed, which allows for uniform cooking.
Whole chickens and turkeys, large roasts, and other larger portions are typically cooked using the indirect method to ensure the food is thoroughly cooked without burning the outside. Poultry especially will burn quickly over direct heat and yet the inside is not up to a safe eating temperature.
You want your bird to have a crispy and browned skin but you probably do not want it charred to the point the skin is burned away and the inside still raw. The indirect method is simply another way of roasting your food.
You can put an empty pan under the food when roasting to catch the juices so you can make gravy or create a sauce from the drippings. You can add water, apple juice, orange juice, or some other liquid to the pan to create more moisture and to add some flavor and to keep the pan drippings from burning away.
You can also add smoke flavor to your foods using the indirect cooking method. Soak wood chips or small chunks in water before adding to the coals to prevent flare-ups and to create a moist smoke that will penetrate into the foods and to keep the wood smoking longer. Dry chips will flame up and burn out quickly adding little smoke to the foods.