The "Prana" (vital force or life energy) flows through our bodies in numerous energy channels. In Sanskrit these channels are called "Nadi's" and in different ancient scriptures is stated that there are between 72.000 and 350.000 Nadi's running through our bodies.
Three of them are called Sushumna, Ida and Pingala. They have a lot of importance in our Yoga practice.
Sushumna is considered the central main Nadi which runs from the pelvic floor through the spinal canal of our spine to the upper skull between the left and right hemisphere.
Ida also originates in the pelvic floor and runs over the left side of the body to the left side of the nose and represents the moon, which stands for female energy, coolness, creativity, calmness, relaxation and regeneration. Pingala runs over the right half of the body to the right nostril and stands for the male principle, the sun, warmth, activity and rational thinking.
Along the spine are seven spots where Sushumna, Ida and Pingala cross. These seven crossings are called Chakras and can be seen as spinning energy centers with different physical and mental functions.
Because Ida and Pingala run through the different nostrils (Ida left & Pingala right), we can influence the activity of Ida and Pingala by breathing dominantly through the respective nostrils. In general the dominance of the nostrils changes naturally at regular intervals throughout the day (every few hours). By paying some attention you can become aware of the dominant nostril. But you can also influence the activity purposely and use the effects.
If we breathe more through the right nostril, Pingala, the sun, male, active energy gets dominant. Therefore it is said that we can think more rational, are able to convince better, and can digest meals better in phases of right nostril dominance. On the other hand, if we breathe more through the left nostril (Ida), all activities associated with the moon are easier. We tend to be more calm, creative and intuitive.
If both nostrils are approximately equally active, we are in a balanced state and inner contemplation / meditation is easier.
Depending on the effect you want, you can lie either on the right side of your body, or on the left side. If you lie down on the right side, your left nostril will open up more and Ida will become more active. That calms you down and enhances your empathy and intuition.
To keep you calm after your Asana practice and after Shavasana, we usually turn to the right side. Like this you stay calm, creative and empathetic for longer throughout the day. The state of relaxation and calmness should not be interrupted by your right nostril sun energy. Another reason for turning on the right side after Shavasana is, that the heart lies slightly more on the left side of your body. By turning on the right side of your body, your heart will get less compressed. This lowers the pressure and strain on your heart and enables it to circulate the blood with less effort.
However, if you want to be active and go out with friends right after your practice, consider lying on the left side instead, to activate your right nostril and Pingala/ the active, rational sun energy.
In order to balance Ida and Pingala and to calm and clarify the mind, you can practice alternate nostril breathing (Nadi Shodhana) or Anuloma Viloma Prana Yama (with holding the breath). These balance the energies and enhance your concentration and focus. However I would recommend to learn these with an experienced teacher before practicing on your own. And keep in mind - never push or strain.