When building a charcoal fire, you can arrange the coals so that one part of the fire is hotter than the other: All you have to do is bank most of the hot coals to one side of the grill or on the outer edges of the grill, in effect creating a two-level fire. This gives you the option of direct grilling (putting the food right over the coals) or indirect grilling (putting the food on the cooler part of the grill, farthest from the hot coals, and covering the grill to create an oven-like atmosphere).
You can also create this effect on a gas grill by keeping one or more burners at medium-high heat and one at low heat. By building a two-level fire, you have the flexibility to move food around if it's cooking too quickly or slowly. Even hamburgers, chicken breasts, butterflied chicken, and steaks—which should be grilled quickly over direct heat to stay juicy—can benefit from resting on a cooler part of the grill.
Indirect grilling is the best method for cooking tougher cuts like ribs that benefit from long, slow cooking or large roasts and whole chickens and turkeys that would burn on the outside before they're fully cooked inside if grilled over direct heat. On a charcoal grill, they need a large spot on the grate that isn't directly over the coals, so put a large foil pan in the center of the bottom of the grill and arrange the coals around it (the pan also catches dripping juices from the roast). You can also buy metal brackets that hold the coals to the sides of the grill. On a gas grill, put the roast or chicken on a rack inside a foil pan and put the pan directly on the grate.