Turn on the television and you're likely to see broadcast journalist Linda Ellerbee using it. Open your mail and you're likely to read about how much International Business Machines Corp. and Sears, Roebuck & Co. want to sell it to you.

What famous people are using and big companies are selling is a new computer service called Prodigy from an IBM-Sears joint venture called Prodigy Services Co. of White Plains, N.Y.Prodigy is a videotex service that connects personal computers through normal telephone lines to larger information-packed computers. It is designed to let consumers shop for groceries, make travel plans, buy stocks, play games and write messages to Jane Fonda by using their personal computers.

The multimillion-dollar ad and direct-mail campaigns for Prodigy were launched in September, when San Jose became one of seven start-up cities for the service. Thirteen more cities will be added by next year, but for now Prodigy is predominantly a California service. Prodigy is also available in Los Angeles, Santa Barbara, San Diego, Sacramento, Atlanta and Hartford, Conn.

Several other companies have tried and failed to make videotex services profitable. Bank of America offers a computerized home-banking service but has been unable to attract more than about 20,000 subscribers.

Other companies floated trial balloons that burst before the videotex services made it to market. For instance, Knight-Ridder Inc. - which owns the San Jose Mercury News - shut down its Viewtron videotex service in March 1986. It spent $50 million on the venture to come up with only about 20,000 subscribers since 1983.

But Prodigy officials believe that 1988 is the right time for the right videotex service. "Nationally, there are 7 million personal computers in homes," said Ross Glatzer, senior vice president of membership marketing. "We're in this business to attract tens of thousands of those users."

Prodigy officials believe that other computerized services are too expensive and too difficult to use. Services such as Dow Jones News-Retrieval and CompuServe charge users for each minute they use the system, which can quickly add up to $50 or more per month.

Prodigy is different from other computer services because it is based on "a classic publishing model," Glatzer said. Users pay a flat fee of $9.95 per month no matter how many hours they use the system. The remaining cost of the system is picked up by the 125 advertisers who pay to be on the system along with the news, sports and weather.

The user sees a different advertisement each time a new computer screen is called up. The ad takes up about one-fifth of the screen, but the user can expand the ad to fill the screen.

Using ads to finance the cost of delivering information is an old idea for newspapers and magazines but a novel way to keep costs down for a computer service, said Andy Bose, vice president of research for the market research firm Link Resources Corp. of New York. "Ultimately, Prodigy will be successful based on its advertising revenues."

To make the system easier to use, Prodigy paints the screen with computer graphics and clearly labeled menus. Help is available on-line at the press of a key.

The graphics are produced in part by software running on the personal computer that was developed by Prodigy programmers. The software is available through the mail and at most Egghead Discount Software outlets for $49.95. A $150 version of the software is available for users who don't own a computer modem, which is necessary to connect the personal computer to the service.

Unlike most computer services, Prodigy is not aimed at hobbyists who like to play with computers or businesspeople who have a pressing need to use such a service. Prodigy is aimed at the average consumer.

Prodigy is designed to save busy people time with services such as Grocery Express. Users connect to the grocery delivery service and transmit their grocery list to a delivery service. The service dispatches shoppers to buy the groceries and then deliver them to the Prodigy user.