Whether these old shares or stock certificates have any value depends upon whether the company is still active. Even then, who may not be able to sell the shares if they are not in your name.
If you want to go it alone, then you may need to do quite a bit of research, and you will need to check the certificate for: Company name, location of incorporation, the CUSIP number the name of the person with whom the security is registered.
Check the company's name against the stock market page in a newspaper or the automated ticker, which can easily be found online. If you find the company's name, and you are legally entitled to sell the shares, then all you need to do is talk to the investment officer of your bank, you will be able to arrange the sale.
What If I Can't Find the Company's name?
The company may have gone bankrupt, or is no longer a Public Limited Company, in which case your certificates are worthless, unless you find a collector willing to buy them on eBay.
However, the company may still be trading on the stock exchange under a different name, the result perhaps of a merger or takeover. To find the company's name, consult a book such as the Directory of Obsolete Securities or the Robert D. Fisher Manual of Valuable and Worthless Securities.
If you are able to find the company's current trading name, you will need to contact a transfer officer of that company - you should be able to find a name on the company's website.
They will guide you as to what to do next in order to sell the shares.
Here's a short film telling you more: