The post-war years witnessed a "freedom explosion" across the globe, especially in Asia and Africa. Why did several of these new nations turn to the Soviet Union rather than the United States for support

Answer 1

One reason was idealistic; the communist philosophy appealed to some nations that had been ruled with no regard for workers and their rights.

A more important reason, though, was economic. The USSR and the US often vied to see which one could offer the most to these emerging nations.

This article reports a fairly typical situation.

http://en.wikipedia.org/wiki/Aswan_Dam#Aswan_High_Dam_Politics_and_Funding