I've smoked one on a Weber charcoal grill. I used a smokenator, a piece of steel that acts as a shield between the meat and the hot coals used for indirect cooking. Turkey was very flavorful and moist. Between the weber grill and the smokenator, it's a minimum investment to try it out. Nowadays I just dry brine and spatchcock the bird. Good flavor, moist bird, minimum fuss.
I did one on my Weber once - a monster, wrapped in bacon, stuffed, etc...No smokenator (how can anyone do that to the English language...) but indirect cooking. End result was a good bird, but it cooked a helluva lot faster than the veggies we had to go alongside. Damn bbq...everything is either over or under.