The basic message of A People's History is to choose major (usually very well-studied) events in American history, retell them in a way that emphasizes the role of working class people and minorities, and then to show how in each event, elites acted in a way to secure their own power. The Civil War, for example, was hardly a crusade for freedom. Business interests tolerated slavery until they feared a generalized revolt of slaves might spark class warfare. Similarly, the United States only entered World War II when it seemed that Japanese expansion threatened its own empire. He also highlights the devastating effects of American bombing on civilian populations, drawing, in many ways, parallels with Axis atrocities.
Zinn's problems with evidence and interpretation are well-known. It is generally regarded as very sloppy and simplistic history even by leftist historians like Michael Kazin and Eric Foner. (Kazin's famous scathing review of a recent edition of Zinn's book in Dissent magazine is linked in the reference section below) but his message has influenced generations of history students, and is in many ways a wonderful introduction to the last half-century of work by social historians.