How does the stock market indexes work? How do you compute for the stock index?

Answer 1

First order explanation:

DJIA weighs against the stock price for the 30 companies it tracks. For example Stock A is $40/share while Stock B is $20/share Stock A's movements will affect ~ 67% of the two stock "DJIA" index.

S&P 500 weighs against the market cap of companies. Therefore one ultra-cap company will have a dominate affect on the index movement verses many less large cap companies.

I only talked about two major indices but the formula for calculating their "price" is pretty involved.
Check out some books on stocks and indexes or visit websites like investopedia.com, fool.com, etc. Also the indices and stock exchanges have their own websites which will go into more detail.

Answer 2

The Dow Jones index is the oldest and simplest one, it is an arithmetic average over 30 major companies.

Other indexes like Standard & Poor's 500 is a weighted average over 500 major companies.

Every company has an specific weight in the index, depending on how active it is, the more active, the more representative.

So, every trade on one of these 30, or 500, in each case will affect the index in the proportion of that company and the wight it represents in each index.