Check to see whether the stock certificate has value as an investment or simply as a collectible. If the certificate no longer represents actual equity in a company, then sell it to a company such as Scripophily.com.
Look at the front of the stock certificate. If it represents a real share, it has the purchaser's name on it. It should also have the name and location of the company and a CUSIP number. This last piece of information is a unique number assigned to each security. If the company is still around, research its current status on the Internet. If the company name is from an entity that no longer exists, talk to a broker, who can look up the CUSIP number for you.
If it turns out that the stock is for a defunct company, or you have no way of proving that the shares in the stock have been assigned to you, contact a company such as Scripophily.com. These companies buy and sell old stock certificates, providing a market for hobby collectors, also known as scripophiles. If it turns out that the stocks still have equity value in a company that you can claim, establish an account with a brokerage to allow you access.