Water, water, water
Don't risk dehydration - make sure your pet has an abundant supply of fresh drinking water (use a few bowls if you're out of the house during the day). On particularly hot days, add a few ice cubes to avoid the water heating up too quickly.
Time your walks well
If your pet needs regular walks, time them with the coolest parts of the day: early morning and late evening. In the hottest parts of the day, they should be in a cool indoor environment.
...and don't over-exert them
Most pets need plenty of exercise but it's okay for them to be sedentary once in a while - particularly in scorching hot weather. Don't feel guilty about skipping high-energy playtime on extremely hot days but remember to make up for it when the weather is cool again.
Never leave your pet in the car
This one should be a given but you'd be surprised how many pet owners don't heed this advice. Pets shouldn't be left in any unventilated space (including high-rise apartments without adequate shade and airflow - leaving a fan on during the day is a good way to combat this), let alone a tiny car. If you're driving with your pet on a hot day, make sure you bring plenty of water and take regular breaks to make sure they're coping.
Keep up grooming routines
Not only does matted fur look bad and create discomfort for your pet, it also traps heat. Brush your pet daily (particularly long-haired cats and dogs) to ensure there's heathy airflow through their fur. If you're dealing with a cranky pet, get the brushing out of the way first thing in the morning, before the heat kicks in and causes extra moodiness.