Alternate Nostril Breathing is one of the many different yogic breathing techinques. It can help to calm your mind. A few rounds can be a great stress reliever and a great way to begin your meditation practice. It can even help to restore balance in the right and left hemispheres of the brain!
I have to be honest, when I first saw this breathing technique in a yoga class, I was skeptical. I thought it was really weird and really did not want to participate in it. All I can say is that some things in yoga are a little weird if you don't know what they are or aren't used to them. But learning about the benefits and trying them for myself have proven to me that they are worth doing anyway (look, I'm even posting pictures of this strange breathing technique that I didn't want to be seen doing, so I would say I am a believer now!).
The top picture shows the positioning for your hand (use whichever hand is more comfortable). You typically start with the first two fingers down (but for some people, they need to bring the first three fingers down, so if that is you, just replace "pinky" where I say "ring finger").
This technique should be done slowly and mindfully, never quickly trying to rush through it. It really only takes a few minutes. I think it feels best to close your eyes. If this ever makes you dizzy or feels like it isn't for you today, open up both nostrils and breath slowly but normally. I've tried this when I've had allergies and it wasn't exactly the greatest time to do it. So, just like with everything else in yoga, listen to and honor your body.
Start by placing your ring finger to close off one nostril. Always keep one nostril open during this. Inhale through the open side. Close off the other nostril with your thumb and open the first side. Exhale through the newly opened side. Inhale through that same side. Close off the other side with your ring finger, open the side with your thumb, Exhale through the open side. And you simply repeat this sequence.
So, every time except the first time you:
EXHALE through the open side, then
INHALE through the open side
and move on to the next side (close off the other side, open up the one you were on and do it again).
(the first time you are just starting so you only inhale)
Once you have completed several rounds (say 5-10 on each side), gently place your hands in your lap. Inhale and exhale, slowly and calmly through both nostrils. Check in with your body and notice how you feel.