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.