Wear light colored and loose fitting clothing. Dark colors will absorb the heat and make you hotter. Skip mesh clothing or tank tops, they don't offer enough protection against the sun. The ideal fabrics are ones that help with heat loss and evaporation. Cotton, acrylic, ClimaLite, CoolMax, Ingeo, polypropylene, PrimaLoft, Sensura, Thermax, Thorlon and Wonder-Wick are all reasonable moisture wicking fabrics.
Bring along a towel to wipe the sweat off your face and out of your eyes. Sweat cools you down by carrying away heat as it evaporates. If it's humid outside, there's less evaporation of perspiration so it's good to use a towel to wipe the sweat away. You might even consider a wet bandana around the neck to help keep you cooler.
Don't forget a hat and sunglasses. The hat should have a brim to keep the sun off your face and use a strap with your glasses so they don't fall off as you exercise.
Warm up and cool down like normal. The sun may feel hot on your skin, but that doesn't mean your muscles are warmed up. When you cool down, bring it inside where there's a breeze or air conditioning.
Ease into your summer routine. Start a little slower and give your body plenty of time to adjust to the heat.
Avoid the hottest parts of the day. Depending on where you live, it can really start to heat up after about 10:00 or 10:30 in the morning. Then it usually doesn't begin to let up until after 3:30 or 4:00 in the afternoon. But if that's the only time you can exercise, look for shade. It can be as much as 10 degrees cooler in the shade of a tree or under a forest canopy.
Remember there are 24 hours in a day. There's nothing written that says you can't exercise after the sun goes down when it's typically much cooler. As long as you're in a safe neighborhood and you wear reflective clothing so you're easy to spot, a nighttime jog can be both refreshing and peaceful.
Be aware of the heat index. That's a measure of the temperature and humidity. If it's above 90, keep your workouts shorter. If it's above 105, hit the water or workout inside.