Common stock is simply a claim on a company's future dividends. There are two kinds of stock: preferred and common. Common stockholders receive a pro-rata share of all dividends the company issues after preferred stockholders and bondholders have been satisfied. They also receive a vote in periodic elections for the board of directors, which governs dividend policy. Eventually, you may want to redeem your shares -- that is, exchange them for cash. The way you would go about this depends on the company.
Visit a stockbroker. A stock broker is an individual licensed by the Securities and Exchange Commission (SEC) to act as an agent for the buying and selling of securities. In this case, he would need to hold a Series 7 license, which authorizes him to buy and sell individual stocks, as opposed to mutual funds and variable annuities. The stockbroker will attempt to find a buyer for your stock, in exchange for a commission. For this approach to be effective, though, the stock must be publicly traded.
Go directly to the company. Some companies will buy back publicly floated stock from shareholders -- particularly if they perceive their stock to be undervalued. This has the effect of creating a market for stockholders, while increasing potential earnings per share for remaining shareholders. Contact the investor relations department of the company, or the human resources department if you are or were an employee.
Approach other shareholders directly. They may be willing to purchase your shares directly from you. This process is much easier among small business shareholders if there is a buy-sell agreement in place, governing how a shareholder may exit the business, and how his shares will be valued in the event of a buyout.