Picture a sleepy, snowy Saturday morning in early 1988. The family has planned a shopping outing, but those plans have to be scrapped.

While the coffee is brewing, the home security system, which is hooked up to the cable television apparatus, is checked for any flashing lights indicating possible burglary attempts during the night. The television set is flipped on to the all-news station. In 15 minutes, the station has broadcast reports from Europe and a glimpse of the weather across the country.

The family slowly heads for the breakfast room. The television control box is punched with a code number, depositing a paycheck and adjusting a savings account, performing tasks that would have been done that morning at the bank's branch office. As an afterthought, the family bookkeeper pays the monthly cable televison bill of about $130 through the cable hookup.

The kids are getting anxious, so, for about an hour and a half they watch on their TV set a new children's movie they've been wanting to see at the local cinema. It costs about $3.50 for the two of them.

After the movie, area shopping information is called up on the screen. The latest specials from the local department store are examined and boots are ordered for the kids, again using the home shopping computer linked with the cable television system.

A check of the 200-page cable programming guide indicates that Dad's alma mater, 2,000 miles away, is about to play for the conference basketball title against a major rival in the Midwest. The game is carried by one of the three all-sports networks. For 50 cents, the game is brought in.

By now it's getting into the evening, and the family decides to settle in for a hot musical still playing its first run on Broadway. The musical, interrupted by a single intermission, is followed by a package of advertisements. It's now about midnight, the kids are tucked away and their parents decide, again for $3, to tune in that X-rated film that played at the theater into which they wouldn't dare venture.

Is this a typical day later in this decade? In some hamlets around the country, pieces of that scenario already are being playout out, experimentally, with the cable television industry the focal point for the sweeping changes in the fields that bring electronics into the home.

The nation is in the midst of a dramatic communications revolution, a multibillion-dollar chess game that is altering the makeup of the broadcasting, film, news and information industries, and one that could ultimately shape the way we conduct business, learn and entertain ourselves.

"We will walk away from television as we know it today," said Gustave Hauserr, chairman of Warner Amex Cable Communications Inc., a partnership of Warner Communications and American Express Co.

In 1981, the cable television industry plans to spend close to $1 billion wiring the nation. Spinoff industries, such as those that supply equipment, programming, financial resources and advice, share in what may become America's most lucrative and potentially profound industrial construction project since much of the nation's telephone and railroad industries linked the nation almost 100 years ago. Until 1980, the total investment in the cable industry was about $3.5 billion.

Cable industry revenues are expected to rise by 60 percent this year, from $1.5 billion to $2.4 billion, still far short of the $11 billion network television business. But by 1988, total cable revenues are expected to rise to about $14 billion.

So the banks, insurance companies and other financial institutions are scrambling for cable business. And the media giants, film companies, satellite builders and others are scrambling for a piece of the growing cable pie.

But regulators, educators, industry officials, citizen groups and virtually everyone else concerned with communications are wondering aloud what the wiring of the American home, whether that new powerful link comes from the cable or the telephone industry, ultimately will mean for society.

"This will rival the Industrial Revolution in terms of changing the world," said Chris Weaver, science and technology vice president of the National Cable Television Association, about the cable industry's role in what is certain to be a technological and information revolution. "But the weakest link in the whole system is the human being. We're the potential problem."

"The potential of cable television in a wired city for improving the quality of life for the average citizen is enormous," said Samuel Simon of the National Citizens Committee for Broadcasting. "What is potentially extraordinary about cable is its ability to demystify the whole television experience and get people to use it and not just watch it."

The key to who will control the direction of that revolution is the wiring of the American home. It could be the newly developing cable television industry, equipped with a sophisticated coaxial wire with the capability to bring a variety of different types of signals, television pictures and data, into the home. It could be the telephone industry, with an older, less sophisticated wire, but with access to nearly all American homes. But the link to a plethora of services is coming, inexorably.

"It's either their wire or our wire," Hauser said.

Although the Federal Communications Commission has proposed permitting telephone companies to compete for cable franchises in sparsely populated rural areas, American Telephone & Telegraph Co. has said little about what it would like to do to put information and data into the American home.

But the prospect of the resources of AT&T, the world's largest company, entering the battle has spurred the cable industry to move quickly to develop its technology to make the wiring of the nation more than just a service to provide people with movies and other entertainment forms.

The Bell System, cable experts note, has demonstrated the value of having a wire in American homes and businesses, and that wire is used across the country to connect computers, copying machines and other devices that for now are the initial link in the wiring of the nation.

"We have not created the demand for data. Others, primarily Bell, have," said Robert Wright, president of Cox Cable. "They're really the only game in town, in that regard."

But for now, with the telephone company's role in the home information and entertainment market unclear, the cable industry is pursuing a series of activities once considered "blue sky." Take these examples of cable's potential:

In Columbus, Ohio, Warner Amex is operating the nation's first two-way cable system: QUBE, a service that provides television shows and data and allows viewers to respond immediately to polling and other "interactive" programs via their control boxes.

Viewers have had a score of unique opportunities, including a recent show that allowed subscribers to call the plays during a semi-pro football game. QUBE's capabilities and operations have encouraged virtually all cable operators to propose such systems in franchise competition, and has clearly given Warner Amex the impetus to gain large chunks of franchise areas in major communities such as Dallas, Pittsburgh and St. Louis.

Cox Cable Communications Inc. is experimenting with its "Indax" system, in which a pilot program on the company's San Diego cable system includes a way to link the cable system to home management, where the cable will be able to control energy usage and provide home banking and shopping.

The American Educational Television Network is broadcasting, via cable, for-credit courses to potentially millions of people (doctors, lawyers, firefighters and real estate brokers, for example) who need access to continuing education programs.

In any number of cities, cable companies are offering municipal governments direct hookups with subscribers. In Dallas, where Warner Amex, pending a possible local referendum, won the primary city franchise, Warner Amex has pledged to offer two "city access channels" for possible broadcast of city government meetings and a second channel for possible use by the Dallas Public Library for the distribution of literature. Similar pledges have been made in many cities across the country.

But the cable industry also has its competitors. Segments of the communications industries are moving to transmit other types of signals into the home to supplement conventional commercial television and perhaps beat cable to communities awaiting its development.

Communications Satellite Corp. (Comsat) has launched an ambitious $600 million program to provide the first direct satellite-to-home broadcasts with a plan to market relatively inexpensive signal receiving dishes across the country.

The Comsat plan, which would offer three new original programming networks to consumers, could be operating within a couple of years in a clear effort to slice off a piece of the cable television market.

At the same time, the Subscription Television (STV) industry is also moving quickly to market its services, which combine conventional television signals with a small box attached to the television set. That box decodes a scrambled signal of pay television fare similar to what is offered on many cable television systems. STV is growing by a rate of about 65,000 homes a month.

"There is a myth that cable television will stop our young industry," said Rinaldo Brutuco, chairman of the Subscription Television Association. s"However, it is not our intent to battle cable television, but rather to coexist with it in the overall marketplace. There is more than ample room for both."

While all these changes are altering television signal delivery, the nation is also seeing a boom in consumer interest in other home entertainment and information devices, ranging from discs, which on the home TV set show arts performances and films and offer computer games, to home computers that manage family finances.

And with that boom comes a wide variety of opportunities for new companies to produce programs for television. Dozens of new and old companies are producing shows for cable, including two of the three major commercial television networks, which putting together cultural programming services.

On the local level, too, news and public affairs shows are being produced by groups previously unable to bring television attention to their communities.

"I can see the day when the young journalist will look forward to 'owning' a community cable telecast just as my generation dreamed of owning a country paper," CBS anchorman Walter Cronkite said recently.

But only with time will even communications experts know which of the technologies will survive. Nevertheless, the cable industry is busily building its entertainment and information network across the country at an unprecedented rate and is generally regarded as having a distinct advantage over the competitors: the technology to bring dozens of signals to the home or to businesses, schools and other institutions.

Yet, about three-quarters of the homes already hooked up to cable television have older 12-channel systems largely dependent on conventional commercial television. So even in those markets, unless those systems are rebuilt at extraordinarily high cost, the competitors have opportunities to make inroads.

"We feel that the industry of the '80s is the cable industry, but what's really happening is an explosion in the consumer's home," said David Wicks, a financial analyst and a leading cable industry investment broker with Warburg Paribus Becker in New York. "In 10 years there will be numbers of channels being talked about that we can't even conceive of.

"The home will be like a library with a screen, a phone, a computer, a printer and a video machine. The consumer will have in his home a variety of devices, but all are going to be tied into two wires: the telephone and the cable. It's getting down to the fact that this is the communications industry, and everybody is going to want to be a part of it."

With those kinds of opportunities, it is easy to understand why many of the nation's largest conglomerates, ranging from media giants like Time Inc. to oil companies like Getty, have become involved actively with the cable game.

But the deep-pockets financing of the industry by wealthy corporations has also prompted fears about what is thought to be the inevitable economic concentration of the cable television business, now virtually free from FCC regulation, which earlier in the 1970s was more a cottage industry than a Wall Street megabucks field.

The public is also asking significant questions about the nature of the industry: whether, for instance, its programming will simply mirror the standard fare of the networks, and what role the networks, which are seeking to program, supply services for and own cable systems, will play in cable's development.

Local governments, snowed under by sophisticated conglomerate representatives and aggressive consultants, are waging internal wars, fights with the press and sometimes with the law over the franchising process, the process that ties the cable industry's wires to the nation's streets and ultimately to the home.

The publicity over those often ugly, occasionally scandalous and frequently unseemly multimillion-dollar franchising fights has prompted a growing nationwide concern about the consequences of these battles for local licenses.

That concern, increasingly expressed by top local and federal officials, ultimately could throw a huge roadblock, primarily in the potential development of new federal regulations, into an ongoing technological and regulatory revolution, top industry officials say.

"The corrupt nature of franchising is threatening self-regulation," a top industry official admitted.

And, perhaps most important, the industry, blessed with dynamic technological advances in cable wiring, satellite communications and a public apparently eager for additional home entertainment options, must, over the next few years, match the pledges it has sold scores of American cities.

"I fear we are making promises we cannot keep," said Raymond Joslin, president of the California Cable Television Association, in a recent speech.