The basic thing of vocal music, whether North Indian or South Indian, whether classical or commercial, whether Bhajan or Bollywood songs, is the control of our inspiration and expiration, i.e. the total respiratory process. The more control we have on our own respiratory process, the more efficiently we can sing.
So the primary lesson of vocal music is a regular practice of Pranayam which should commence after a relaxed phase of respiration in a comfortable sitting position for at least 4 to 5 minutes.
While practising, the spinal chord should be erect and the face straight. It would be better if you could keep a mirror in front of your face so that you can visualise your facial expression while you sing. This is because Music is a performing art and you should sound well as well as you should look presentable too while you perform.
The next phase includes the practice of standing notes and then comes the vowels (step by step) in different techniques.
You have to understand that different vocal exercises improve your voice in specific parameters. For example, the vocal exercise to improve the tonal quality of your voice will not help to add flexibility to the same and vice versa.