• Don't damage a living tree. Look for sticks on the ground.
• Choose a stick that is long enough so you don't get cooked in the fire too!
• Make sure that it is sturdy enough to support your meal.  The bigger the item, the thicker the stick (or you may want to consider multiple sticks).
• Carefully whittle away a few inches from the end to clear off the outside bark and make a sharp point. 
• Skewer your victuals, cook, and enjoy!

Tips:

• Take your time, your food should be kept far away from intense flames in order to cook slowly.  Cook too fast and the center may not get done.  The time will allow the heat and smoke to cook your food evenly and add flavor. 
• If your food item has a skin on it, try to keep the skin in tact in order to prevent moisture loss. 

Sources:

• http://www.thecampingfamily.com/marshmallow-roasting-sticks.html
• http://www.nytimes.com/2015/07/01/dining/campfire-cooking-roast-on-a-stick.html?_r=0