How NSE Works?

Getting straight to an example:

Lets say you own a private company that makes shoes. The demand for your shoes increases and you estimate that you need more working capital to meet the demand. So you plan to turn your company into a corporation and go public. You go to the state government to get a charter and permit to form a corporation. Now you would go to an investment bank and show your project report and capital requirement estimation. The investment bank promises to help to sell your shares. Then you and your banker would go to SEC in Washington  for getting an approval on the authenticity of the corporation. After the SEC approval your banker gives you the required capital investment in exchange for shares. The investment bank now sells the common stock of the shoe corporation and you expand your production to meet the demand. The people who now own the common stock are proportionate owners of your corporation's assets and they elect the board of directors for the company. These board directors monitors the functioning of the company and decides upon the dividends to be paid to the stock holders from the earnings of the new expanded company. 

Now lets say your company is really doing well and the demand increases more and you are in need for more capital. One way is to issue more shares and raise capital and the other way is that the stock holders elects a president and send him to New York stock exchange to see if they could qualify to be listed in the exchange and could allow trading of its securities. The selection committee then makes the through examination of the company's records and further business capabilities. Once it is approved the securities are now traded nation wide. Now if someone wants to buy your company's shares you would contact your broker and he contact his partner in the exchange and tries to negotiate on a price with someone who is interested in selling your company's shares. This is how the stocks are traded.