To grill vegetables well, it is a good idea to coat them in oil, use a skewer or grill basket and slice them in a way that maximizes surface area. Some other tips are to marinate or season vegetables before grilling, to use foil packets and to precook hard vegetables.
Vegetables can stick to the grill easily, so give them a light coating of oil beforehand to prevent this from happening. Try using skewers or grill baskets for small vegetables, such as cherry tomatoes and mushrooms. This can keep them from rolling off the grill or falling through the grates. Slicing vegetables into large, thin pieces allows more area to touch the grill. This helps the vegetables cook faster and usually results in a more flavorful dish.
Marinating vegetables or sprinkling them with seasonings before grilling them can add a lot of flavor and prevent them from drying out. Vegetables, especially smaller and more tender varieties, can burn quickly. One way to cook these on the grill is to steam them inside foil packets. Hard vegetables, such as carrots and potatoes, can be partially pre-cooked to make their grilling time shorter. Boiling them for a few minutes is usually sufficient.