Ask ten people how to cook ribs and you'll probably get fifteen different answers. You can do 'em in the oven, you can rub 'em down and grill 'em up, you can marinate 'em, start 'em in the oven and finish 'em on the grill, braise 'em, or figure 'em out all sorts of other ways. As for types of ribs, though, I'd argue there are but two choices: pork spare ribs or beef ribs. Baby back ribs, though popular, are overpriced, lack meaty worth and therefore miss the cut.
Tonight, I'm barbecuing beef ribs, although a similar method would also work for spare ribs. Lots of folks go for rubs, and if you do to, I'll leave that up to you. Mixtures that combine cinnamon, salt, pepper, brown sugar, cumin and such seem to be the usual suspects. For me, though, sauce is where it's at, so I'll focus on that after navigating the nuances of the grill.
I go for a slow "roast" on the grill to tenderize the meat and also to provide it with a subtle smoky mistress. Start with a bank of coals. Since this is a slow roast operation, you won't need too many. All you need is half a chimney full, which is about two or three handfuls. Let them glaze over with white ash, and then pour them out into an embankment along one side of the grill. The bank allows for far superior control over the heat than stacking them in the middle of the grill. You're ready to throw the ribs on when the coals cool to the point that you can hold your hand over them for several seconds without being uncomfortable.
Then roll out the ribs after seasoning, either with a rub or just salt and pepper. I usually arrange them as far from the heat source as possible, which means, practically speaking, around the circumference of the grill. See the photo below for an example. You'll of course want to rotate the ribs so that the ones that start closest to the coal bank get moved out, and the others get moved in.
Add soaked woodchips to the bank a few at a time. You need not smoke the joint out, but you want to get a good waft workin' through the top vent. Continue to add chips a few at a time throughout the cooking process. Also, add charcoal briquettes three or four at a time to keep the fire going once the newest round of coals has ashed over.
You want moist and tender ribs, so be sure to keep the fire small and to rotate the ribs about. Tonight, I left them on for just under two hours, but longer would probably be better. With a hotter fire, they'll of course take less time.

Arrange the ribs round the circumference of the grill, providing as much space as possible between the meat and the coals, which are at about six o'clock in this photo.

The subtle smokiness of a few chips thrown on the coals as the ribs cook imparts a bronze color and toothsome flavor.

A modest bank of coals keeps the cooking temperature down, but will also need to be replenished with a few fresh briquettes as the spent coals cover with ash.

Slathering the sauce over the ribs as they cook enhances the flavor of both.
Now for the sauce, which I paste onto the ribs while they cook. Start with well-caramelized shallots, and add white wine and a tomato puree. Then season with salt, pepper, brown sugar and, if you want some heat, either wasabi or Serrano chilies. Also add some sort of vinegar--white wine, apple cider, balsamic--and some red wine. Allow to reduce and taste as it does so. Lime juice will help bring the flavors together. Adjust seasoning and adjunct mixture until the sauce is deep crimson and well-balanced: there should be acidity from the tomatoes and vinegar, as well as sweetness and a hint of heat.
Needless to say, this is but a road map: molasses, hot sauce, cinnamon, and all sorts of other additions would also be welcome.
Mashed potatoes go wonderfully with grilled meats, as do a few lightly fried shallots.
