Dogs can't sweat. They cool off by panting, so an overheated dog will drool excessively. It will become lethargic, its eyes will be bloodshot, and it may appear a little pale. If you lift its skin, it will take longer than usual for the skin to fall back into place.
Different dogs have different needs when battling the heat. Keep in mind that darker coats absorb more heat than lighter coats. Also, overweight dogs are at higher risk for dehydration. Carry a bottle of water when going on a walk with your dog. Better yet have your dog carry it for you in a backpack or a vest! The water in the bottles will keep the dog cooler and also give the dog a sense of purpose.