Some Asian religions teach that Chakras are energy centers or "wheels" of the subtle body through which prana (subtle energy) is circulated naturally and through meditation, and we have 7 main chakras along our middle. The third eye is the sixth chakra located on your forehead, which is said to be our center of intuition and associated with our pineal gland.
Purported benefits of working this chakra include: enhanced clairvoyance, stronger visualization capability, stronger connection to your Higher Self, improved astral projection ability, and a better perception of subtle energy. There are several ways the third eye can open on its own, but there are meditation techniques we can use to make it happen.
Step one of this meditation is to relax yourself entirely to the rest of your ability. Sit with your back straight in a comfortable chair or lotus position on the floor and breathe in your nose and out your mouth. We want to quiet emotional stress and nagging mundane thoughts which would be a distraction from the meditation. Some people imagine putting these thoughts in a visualized trash can, others envision a pure white cloud floating down from above, pulling away all kinds of stresses and negative energy like a magnet. The specifics of how you see this is your choice. I prefer a dark quiet room for meditation, since ambient lights and sounds make it hard to relax even with your eyes closed. Do what it takes to feel relaxed and comfortable. Slowly feel more and more relaxed feeling each part of your body release muscle tension.
To open the third eye, focus hard on your forehead while you keep breathing slowly and deeply. With teeth slightly apart, people say or vibrate a simple mantra on exhale like TOE or AH, which should resonate inside your head. It may help to visualize a spinning wheel or sphere of light there. Conventionally it is blue, but the exact color is not that important.
Make sure to believe that this chakra will open, even if it takes days or even weeks of using of using this meditation. After being opened the first time, it should stay open or be more easily opened in the future. Some indicators that your third eye is opening are pressure in your forehead, a tingling feeling on your forehead, a perceived change of colored light with your eyelids closed, and ability to visualize your chakras more clearly. Even if you notice none of these changes, make a note of any changes you do experience and see if they intensify with practice.