How do you cook beef ribs?

It depends on the rib. Beef long ribs taste great indirect grilled at a moderate temperature, like baby back ribs (be sure to toss soaked wood chips on the coals). Beef short ribs are better smoked low and slow in a smoker. Incidentally, the Koreans have a fabulous and singular way of cooking beef short ribs: They cut the meat into paper-thin slices, which they grill directly over charcoal—see the kalbi kui recipe.