One of the most valuable pranayama Ayurveda offers is Nadi Sodahana. It is the most balancing and peaceful pranayama I know. This is because it harmonises both sides of the body. Naturally we only breathe through on nostril at a time. About every one and a half hours the nostril you breathing through changes.
The right nostril is solar-pita, and the left nostril is lunar-kapha. Whichever nostril you breathe through will increase that dosha. The right nostril is related to activity, eating, daytime, defeacating...where the left nostril is related to sleep, night time, urinating...Vata swings between the extremes. The idea is to find somewhere in the middle.
It is is said that enlightened beings, those who are self realised, breathe evenly through both nostrils at all times. The rest of us mere mortals can experience brief glimpses of such peace during meditation, yoga or pranayama.
To practice Nadi Sodhana (and you should!) first sit in a comfortable position with your back and neck straight but relaxed. Place your right hand so your thumb is resting on your right nostril and your ring finger is resting on your left nostril. I like to place my two middle fingers on my third eye to focus my attention better, but you can just relax your other fingers.
Begin by closing the right nostril by pressing down with your thumb and breathe into your belly through your left nostril. Now close your left nostril too with your ring finger and hold the breath. Gently release the right nostril and exhale. Inhale again through the right nostril, hold (by squeezing with your thumb and ring finger) and release the left nostril to exhale. This is one cycle, repeat as many times as is comfortable always finishing on an exhalation through the left nostril.
Everyone counts differently, but I am a great believer in not forcing your breathing. As a guide, I usually inhale for five counts, retain the breathe for eight counts and exhale for five. My guru taught me to inhale and exhale to the same count, but other teachers have said to exhale for longer. As long as what you do is regular, conscious and comfortable it does not really matter (in my opinion) how much you count to exactly.
It takes a but of practice and few giggles along the way to become familiar with this routine. But even if it is hard, use it as an exercise to focus the mind, a form of meditation. Imagine it is like a horseshoe in through the left, across the third eye and out through the right, and back again.
This pranayama is an excellent way to begin meditation.