There are various ways of grilling potatoes on your barbecue. One of the most known methods is to wrap the potatoes in a piece of aluminium foil one by one. First pour a tablespoon of olive oil on the foil and then spice it with pepper, salt or other spices according to your taste. Then put the potato on the oil and close the foil by folding it. You don’t have to leave the potato in one piece, you can also slice it.
You can also grill the potato directly on the barbecue. The best way to do this is to slice it in rounds or pieces, but not so thin that they fall through the grill. Rub the potato rounds with (spiced) oil. If you prepare the potatoes in this way, then you will have to constantly keep an eye on them.
Also consider that if your potato is still raw before you put it on the barbecue, it will need quite a bit of time before it is cooked. If you want to reduce the cooking time, then first cook the potatoes or the potato rounds in boiling water for about ten minutes. Then let them drain and lay them on the barbecue. Your potatoes will already be done five to ten minutes later!