After months of work behind the scenes, Norfolk Southern Corp. began a public campaign yesterday to win congressional approval to buy Conrail.

Transportation Secretary Elizabeth Hanford Dole on Friday selected Norfolk Southern over two other hopefuls to buy the federal government's 85 percent stake in Conrail. Her choice has a long road to travel before becoming a fact.

Robert B. Claytor, Norfolk Southern's chairman and chief executive officer, told a Washington news conference yesterday that many shippers in the Norfolk Southern-Conrail area support Norfolk Southern's bid and that he hopes for swift congressional action approving it. He said the purchase would not be anticompetitive and that shippers would benefit.

Harold H. Hall, Norfolk Southern's president and chief operating officer, appeared near yards in Conway, Pa., to meet angry Conrail employes, the Associated Press reported. "I think you're here to placate us and give us false assurances and have us walk out of here happy. But we're not. We don't want you," said Ed Rodzwicz, chairman of Brotherhood of Locomotive Engineers Local 325.

Norfolk Southern estimates that about 2,350 jobs would be lost because of the merger. It said about half of those jobs would go to other railroads after Norfolk Southern-Conrail has concluded Justice Department-ordered divestitures, and that most of the losses would be absorbed through normal attrition.

Hall said there would be no job guarantees, but that he expects few jobs would be lost in Conway.

If Congress approves, Norfolk Southern will pay the Treasury $1.2 billion in cash for Conrail; surrender Conrail's tax credits and deductions; buy labor's 15 percent interest for $375 million; restore Conrail employes to industry wages; pay state taxes that Conrail does not pay; divest itself of track or track-use rights in areas west of Pittsburgh and Buffalo where Norfolk Southern and Conrail now compete; and sign convenants guaranteeing to maintain Conrail properly and to operate it is as single entity.

In other developments yesterday:

* Conrail reported that it had net income of $500.2 million for 1984, its best year ever, and fourth-quarter income of $89.6 million on revenue of $792 million. In 1983, Conrail made $313 million.

Conrail Chairman L. Stanley Crane, who opposes the Norfolk Southern bid and wants to sell Conrail to the public through a stock offering, said "the results underscore our commitment to sound financial performance, which we expect to continue in 1985, even with the possible resumption of state tax payments and higher wage levels."

* F. M. Kirby, chairman of Alleghany Corp., one of the two losing bidders in Dole's auction, said that "we will welcome support for Alleghany's bid from all who find the DOT's choice unacceptable."

Alleghany was endorsed by railroad labor unions, and Kirby contended that "a sale to Norfolk Southern would entail the needless loss of thousands of railroad jobs; create a heavy concentration of monopoly power; deprive shippers of competitive rates, and result in abandonment of service to dozens of communities throughout the Conrail region."

* A spokesman for J. W. (Bill) Marriott Jr., who headed an investment group that also lost in the bidding, declined comment.

Claytor's central themes were that labor would not suffer and that shippers would benefit if his corporation wins Conrail. He said the extensive Justice Department review of the merger, and Justice's letter approving such a transaction with appropriate divestitures, should put the antitrust issue to rest.

CSX Corp., Norfolk Southern's major competitor, has promised to fight a Norfolk Southern takeover. "Anyone can sue," Claytor said. "Winning is something else." He said he expects legislation approving the takeover to include the same antitrust protection the Interstate Commerce Commission would grant if it approved a rail merger.

Claytor also said he hopes Congress moves swiftly and warned that the Norfolk Southern's offer will not be on the table forever. "If at the end of the year we weren't any closer to getting it than we are now, I think I would have to recommend to our board that we forget it," Claytor said.