Well-marbled rib-eye likes an indirect heat
Rib-eye, which is cut from the center of the rib, is the King of the Grill, especially the bone-in variety known as the cowboy steak. If the bone is left long and cleaned, the steak is known as a tomahawk. Make sure to buy a cut that's at least 1.5 inches thick. I like to serve mine with a slice of whiskey butter: mix bourbon-soaked shallots with soft butter, fleur de sel, and chopped parsley.
Ready the meat: Wrap the meat in paper towels to dry off the surface moisture. Just before grilling, brush it with olive oil -- this will prevent stickage and keep it juicy. (Some recommend oiling the grates, but the oil is more likely to burn off, which is why I oil the meat.) Then season with kosher salt.
Grill it up: Sear over high heat on each side for 1-2 minutes. Move the steak to indirect heat (which means that the heat source is equally divided on either side of the food and there is no heat directly under the food -- gas or charcoal). Then cook it for about 15 minutes with the lid closed. The rotating hot air ensures the food cooks through uniformly. (I cook all cuts with the lid on.) How long you leave it there depends on how thick the steak is and how rare you like it. If using a meat thermometer (my favorites are this one and this one), take the meat off when it registers 120-125F for rare, and let it rest for 5-10 minutes. If you like your meat more well done, cook it longer (medium rare: 135F, medium: 145F).