Can a new pvt co issue equity shares at premium

There is no bar in Companies Act.  But you have to take care of Sec.56(viib) of Income Tax Act  1961.  Amount in excess of fair market value of shares will be treated as other income and will be taxed accordingly.

how will be thefair market value determined, whether it is based on Net asset value or any other method

You have  to refer to Rule 11U and 11UA for the methodology  and take CA certificate for valuation under the rules.