Who selects these 30 stocks?

They are selected by the Index Committee.

This committee consists of all sorts of individuals including academicians, mutual fund managers, finance journalists, independent governing board members and other participants in the financial markets. 

How do they select these 30 stocks?

Well, they definitely don't do it on the basis of their individual whims and fancies. Some of the criteria they follow include:

~ The stock should have been traded on each and every trading day (the days on which the stock market works) for the past one year.

~ It should be among the top 150 companies listed by average number of trades (buying or selling of shares) and the average value of the trades (in actual rupee terms) per day over the past one year.

~ The stock must have been listed on the BSE for at least one year.