There are two major points of view on this issue.  

The first holds that President Reagan was the primary mover behind the end of the Cold War.  In this view, Reagan ended the Cold War by pushing hard on the Soviets.  His renewed belligerence and his creation of a new arms race stretched the Soviet economy beyond the breaking point.  By forcing the Soviets to over-exert themselves to keep up with his military buildup, Reagan brought down communism.

The second holds that Reagan was much less important than Mikhail Gorbachev.  In this view, Gorbachev, helped by the basic weaknesses of the communist system, was largely responsible for the end of the Cold War.  Reagan is still important in that he acted as a supportive partner for Gorbachev (through things such as the treaty on missiles in Europe).  However, in this view, Gorbachev and conditions internal to the communist bloc are more important than Reagan.