The solution: Wearing the right type of fabrics is essential. Runners should stick to technical fabrics such as DryFit, Thinsulate, Thermax, CoolMax, polypropolene, or silk. This will wick the sweat away from your body, keeping you dry. It's very important to make sure you don't wear cotton for this layer because once it gets wet, you'll stay wet, which can be uncomfortable in warmer weather and dangerous in cold weather. Your skin is also more likely to chafe if you're wearing cotton.
In the winter, make sure that you don't overdress. You should add 15-20 degrees F to the temperature when determining what clothing you should wear -- that's how much you'll warm up once you start running. In the warmer weather, stick to loose, light-colored clothes.