I think that if you have a textbook or an instructor's resource to assist, I would focus on these elements in addition to what you might find here. The idea of "the second Cold War" refers to Reagan's acceleration of the antagonism between both the United States and the Soviet Union. It also brings to light that because of this, there was a worldwide race to essentially try to "out do" the other. Such a reality committed both sides to different parts of the world in not really assessing whether or not it was right for the national interests for involvement, but rather in defeating the other. The Second Cold War caused the United States to support Saddam Hussein against Iran, President Zia and Pakistan against India, and Bin Laden against the Soviets in Afghanistan. In the end, there was little assessment as to whether or not these commitments were in America's long term interest, but rather seen in the short term context of trying to bring down the Russians. The Reagan Foreign Policy underscored all of this in its assertion that it genuinely believed that by accelerating the pace of the conflict, it could outstrip the Soviet Union and end up winning the Cold War.
Ronald Reagan, upon taking office during his first term denounced the policy of detente, or an easing of tensions between the two Cold War powers. Just like the majority of the Cold War Reagan's second Cold War was largely fought with rhetoric.
Reagan wanted to "win" the Cold War, doing what his predecessors could not. He used terms such as "Evil Empire" to describe the Soviet Union.
A renewed attempt to stop Soviet expansion, the so-called "Domino theory," led to attempts to stop or undermine governments in Nicaragua, Afghanistan, and other third world countries around the world in the 1980s.
By the mid to late 1980s Reagan's stance had softened a bit. He even met with Soviet leader Mikhail Gorbachev in 1985 to discuss arms reductions.
In the end Reagan's strategy worked and the Soviet Union collapsed after Reagan's second term ended. The Berlin Wall, the symbol of East-West tensions for much of the Cold War was torn down in 1990, although some historians believe it had more to with internal political struggles in the Soviet Union than Reagan's policies.