Reagan's approach to the Cold War in many ways was a continuation of the traditional strategy that had prevailed since the Truman Doctrine: containment, modernization of the strategic triad (land based missiles, intercontinental bombers, and submarine based missiles), etc. But in some ways, it was a significant departure.
For one, Reagan did not accept that the ultimate geopolitical goal was containment (preventing the spread of communism beyond its existing borders). He believed the Soviet empire was over-extended and that Sofiet influence could be challenged and rolled back in places like Afghanistan, El Salvador, and other countries on the fringes of the empire.
He also pursued a more aggressive strategic forces modernization policy than some of his predecessors. He revived the B-1 bomber program, which had been terminated by his predecessor, Jimmy Carter. He made a move to modernize short range ballistic missiles and push for installation in NATO.
Reagan was also less committed to the doctrine of mutual assured destruction than his predecessors. MAD presupposed that national leaders would be deterred from nuclear adventures if they were aware that any such actions would cause unacceptable retaliation against their country. The Reagan administration at least flirted with the idea that nuclear wars could be made "survivable" and that it was possible to develop a "nuclear war fighting" capability through a combination of strategic defense, civil defense, and offensive capability, including command and control. Reagan initiated the strategic defense initiative (SDI), pursued for a while a civil defense program, and expressed very aggressive intentions toward the Soviet Union.
Pardoxically, though, toward the end of his time in office, he also engaged in serious arms control and peace discussions with his counterpart, Mikhael Gorbachev. One of his well known expressions was "Trust, but veriffy," and he was also well known for his speech at the Brandenberg Gate in Berlin where he said "Mr. Gorbachev, tear down this wall." The wall did not come down and he Cold War did not end while Reagan was in office, but his actions played an important role in sending the Cold War on path to its end.