Two exchanges, one market
India has two main stock exchanges, NSE and BSE. Most large companies are listed on both. When you buy a share through your broker, the order goes to an exchange, meets a seller at a price you both accept, and the trade is done.
What an index is
An index is a basket of shares tracked as one number. NIFTY 50 follows the 50 biggest NSE companies; Sensex follows 30 on BSE. When people say "the market is up", they usually mean one of these went up.
Who is in the market
Retail investors (people like you), foreign investors (FIIs or FPIs), domestic institutions (DIIs: mutual funds, insurers, banks) and proprietary traders. Their buying and selling moves prices; we track two of them on the FII & DII page.
Settlement
Indian shares settle on T+1: buy today and the shares reach your demat account the next working day.