Whether you're giving him cough medicine, a nutritional supplement, hydrogen peroxide to make him throw up, or just water to rehydrate a sick dog who refuses to drink, this method works neatly:
Have your medicine ready.
Stand to the side of the dog. With a free hand, pull the corner of your dog's lip back and out. Insert the syringe, bottle, or spoon into this exposed "pocket" at the back of his mouth, between the lips and the gums. Tilt the dog's head up slightly so the liquid will drain into the dog's mouth and not forward onto the floor. gently and steadily depress the plunger on the syringe. Wait for the dog to swallow or smack his mouth a bit. That's when you know the liquid has trickled into the dog's mouth itself and he has swallowed it in a safe, controlled way.
Do NOT force liquids straight into your dog's mouth! He could choke or aspirate the liquid.