You can and it is naturally built into to your physiology. What you have to do is exercise a specific way that accomplishes three criteria: 1. get out of breath, 2. experience "muscle pain" from pushing it, and 3., sweat, thus increasing your core temperature. When you do that, your brain will secrete a 400% increase in HGH for up to 2 hours post exercise, as long as you do not eat carbohydrates or sugar during that time.
The ideal way to do this is with interval training which offers a convenient way to achieve this. The goal of training now becomes optimizing HGH secretion. So when you exercise: get out of breath, take your muscles to "failure" by pushing them, and sweat. Intensity is the key word. Do this twice per week and help increase your growth hormone secretion.