As it takes a tip from its past to boost its present, J.C. Penney Co. Inc. also is taking cautious steps toward building its future.

Faced with greater competition than ever in the retailing industry, the retailer slowly is diversifying into a number of other business activities, especially communications, data processing and the service business.

Equipped with some of the most modern data-processing and communications technologies in the retailing business, Penney now is offering some of that to other companies.

For Amoco Oil Co. and other oil companies, Penney is providing its telecommunications system to verify and process transactions on the oil companies' own credit cards. For Citgo Petroleum Corp., Penney is running the entire credit-card system, issuing cards, mailing statements and collecting bills. For People Express Inc., Penney handles all the reservations for calls made west of the Mississippi. It is talking to a number of other airlines to run similar reservation systems.

Meanwhile, thanks to its new satellite network that connects store merchants with buyers at the headquarters to discuss the latest fashion and what stores should order, Penney is now offering its extra satellite capacity to other firms that may be interested in live direct broadcasts to field offices, teleconferences or simply videotape production facilities.

"The driving force behind these businesses is that we have a lot of the technology in place," explained Vice Chairman Robert B. Gill. These activities are "small at the moment, but growing nicely."

And they are rapidly leading to new retailing offshoots. Last week, for example, Penney announced the creation of JCPenney Travel Services, a pilot test in Chicago, that will sell specially arranged tour packages, such as trips to Hawaii, to individual customers.

Following the lead of its major rival, Sears, Roebuck & Co., Penney also has experimented with financial services, offering bank-teller machine services, car loans and certificates of deposit. But these apparently have not proved as productive as the other service businesses Penney is exploring. Despite all these efforts, retailing will remain Penney's core business, Gill emphasized. Like many other retailers who find little new business in the highly competitive cities, Penney is turning to rural America, planning to open the bulk of all its new stores there over the next few years.

At the same time, the company has grand hopes for its catalogue business, which last year contributed $2 billion to the company's overall sales of $13.8 billion. With Montgomery Ward dropping its catalogue business, "I suspect we'll get some ruboff there," Gill said. To guarantee that prediction, Penney plans to open "some additional catalogue sales centers in markets where Ward's had franchises and we had no catalogue desk."

Additionally, the company hopes to expand its Thrift Drug Co. operations that it bought 17 years ago. With many regional drug-store chains now up for sale, "we are not adverse to buying some," Gill said. In the meantime, the company will expand its mail-order drug operations, geared especially to senior citizens who rely on daily medication for blood pressure, heart and other medical problems. Believing it has great potential for growth, the company plans to add two more warehouses this year to the existing one to handle the increased business.

Although Penney Chairman William R. Howell recently predicted that specialization will be the "buzzword" of the future for the 1990s, the chain has no major plans to enter the specialty retailing world in a big way, Gill said. The company recently bought a small stake of the women's apparel chain Alcott & Andrews (Gill declined to say how much, other than that it was less than 25 percent.). But Gill said that investment did not reflect a change in strategy but rather an investment in a company that wanted to open a store in the company's headquarters building in Manhattan.

"We have looked at specialty stores over the years and have not at this point identified a particular niche appropriate for us at this instance," Gill said