How does the stock market actually work?

What is the Stock Market?
The stock market is a facilitator for the buying and selling of securities. The stock market provides a legitimate forum for buying and selling stock. Without the stock market, investors would have to find alternative means by which to trade. The stock market brings the buyers to the sellers and makes quick and efficient transactions possible.

On the Trade Floor vs. Electronically
There are two popular ways to buy and sell stock; on the trade floor and electronically. Most investors have never set foot on an actual trade floor. In fact, most of us have only seen a trade floor on the news or from movies. A group of individuals called specialists wait at assigned stations on the trade floor and receive instructions from their brokerage firms. One specialist speaks for a large group of investors, thus making it unnecessary to do your trading in person. This specialist then relays the selling or purchasing information back to the brokerage, who then informs you.
The New York Stock Exchange (NYSE) is the most popular exchange in the world. The NYSE was founded in 1792 by stock brokers and merchants. The NYSE is a trade floor exchange. Even now there are specialists standing at their posts on the floor of the New York Stock Exchange awaiting instructions and acting in the best interest of the investors that they represent.
Electronic buying and selling of stock is what most investors are more familiar with. In this type of stock market there is no trade floor and there are no specialist calling out purchase or sell prices. Everything is done through an electronic network of brokers or dealers.
The Nasdaq is the most popular of the virtual exchanges. Unlike the over 200 year old New York Stock Exchange, the Nasdaq was only just popularized in the 1990's. Despite its recent creation the Nasdaq carries with it some very powerful companies (such as Microsoft, Dell, and Intel) and can hold its own next to the NYSE.

Primary Market vs. Secondary Market
Trading in the stock market (whether electronic or not) is either going to be in a primary or a secondary market. A primary market is where investors buy initial public offerings or IPOs. An IPO is the first time a stock is issued by a company. This is also the first time that securities are created or that company. A stock can be traded millions of times but there is only one IPO. Initial Pubic Offerings are such a huge deal because the company only offers the stock for sale once. Theoretically an investor could hold on to an IPO purchase forever and take advantage of 100% percent of the equity gained.
Secondary markets are where most of the buying and selling takes place. Once the IPO has been offered the company is no longer involved with the trading. The company has no say or direct influence over the price of their stock after their IPO. The NYSE and the Nasdaq deal with secondary market transactions. These transactions are only between investors. Buying and selling prices are decided by dealers that are acting on behalf of the investors.

The inner workings of the stock market can actually be quite complicated. There are third, fourth and even fifth markets that are all working together. The best way to have the stock market work for you is to team up with a brokerage firm. The brokerage firm can do all of the price negotiations for you. They serve as your advocates in the sometimes cut-throat world of stocks. The National Association of Securities Dealers is a good place to turn to get more information on investor advocacy.