YogaToday created this video. The entire exercise takes 4 minutes and 20 seconds to complete. Basically you breath through one nostril and then through the other nostril. Doing so helps you to calm and relax your thoughts and body!
There seem to be two main variations to the way the people hold the right hand. Basically, you either touch the palm of your hand with your index and middle finger or you use the index and middle finger to touch forehead between the eyebrows. In the YodaToday video, Adi uses the former technique. I’m not an expert but most videos on YouTube show the variation that this video demonstrates. Yoga.dk shows pictures on the homepage with the alternate method.
Also check out this study (pdf) about the immediate benefits of doing Nadi Shodhana Pranayama. Nadi Shodhana Pranayama is the name of the breath exercise and loosely translated means Channel Cleaning Breath. Best wishes!