I won't repeat plot details so I suggest if you haven't read the book or seen the film you read the excellent write-up above first.
A lot is made of The Quiet American being strictly anti-American or opposed to American raison d'etat. I would tend not to see it as particularly anti-American, or even unambiguously anti-anything. This is obvious if you just think about the two main characters and how the reader is encouraged to relate to them - it is impossible to hate both Fowler and Pyle, nor love them completely. They are stereotypes and each of us lies somewhere between the two of them.
It was certainly ahead of its time in bringing up specific criticisms of America - remember, it was written in 1955, after the French war in Indochina was over but before the American war had truly begun. So, the criticisms that America was blindly in above its head in situations that it didn't understand (Pyle gets all his knowledge of the Orient from books, not experience) and America was interfering in places it could do no good were very original. Remember, America had been isolationist up until World War II, and only that event transformed it into the global power we know today.
Many of these criticisms have been repeated for so long that they are now cliches (this does not in and of itself make them incorrect). The one criticism that is so popular today that is missing, and which is projected back on the novel over the decades, is that America is purposefully malignant. The conspiracy theory interpretation of American actions which is now so popular was then exclusive to the Communist world and had hardly penetrated the American consciousness itself.1 So The Quiet American is not an accusation of American malignancy, but one of, if anything, its stupidity.
On a straightforward reading you could almost totally ignore the political element to the story and see it mainly as a love story. Here it is not entirely clear where are sympathies should lie. The Englishman Fowler is the wronged man because Pyle steals his woman, but he arguably brought it on himself through his cynicism and selfishness; anyway these qualities hardly make him likable. The American Pyle is immediately likable, being idealistic and selfless. However, he clearly lives in a world of kitsch, "life without the shit" as Milan Kundera put it. This is exemplified when he gets blood on his shoe from the bombing he just orchestrated, and still can't realize he just killed women and children.
Pyle's actions constantly hurt others and yet he is incapable of realizing this, and this innocence puts him beyond the hatred of even Fowler. This is clear in their personal lives, but also in their relationship to the war. And the battle over the girl, Phuong, is closely related to the battle over Vietnam.
Fowler understands Phuong as a human being, which to him does not sound as wonderful as you girls who wish your men did the same might imagine. His understanding of human beings is that they are cynical, craven, and self-interested. Hence, while he has a deep affection for Phuong (mostly physical), he does not love her in the way only the idealistic young Pyle can. Pyle loves her, but to love so completely is to love the idea of someone, not the person themselves; it is to love an ideal. Hence Pyle describes her as delicate, childlike, and in need of his protection.
Now realize that Phuong is the Vietnamese people. Pyle sees them as childlike and in need of the guidance of the West. He doesn't care that some people get killed on the way to building the democratic Vietnam he so desires because he believes in the end it is the best, and it is impossible to hate him for this idealism, however wrong we think he may be. He doesn't even understand his life is at risk in this crusade until it is too late, but if he did it is doubtful he would go home. He has a sort of courage.
Fowler doesn't get involved in the war, he just reports it. He just wants the war to stop so that he and the Vietnamese can live a quiet life. He has no grand dreams of a national democracy or a Communist utopia, because he believes them beyond the realm of the possible. He is happy to live in a cynical and depraved world because he sees it as the only option. He is realistic and treats the Vietnamese people as he treats Phuong - as imperfect human beings that act as such. In the end, he wins, but is this really best for Phuong, who wanted so much to see those bright lights in New York? And is it best for the Vietnamese, who we know suffered prison camps and death, rather than those bright lights in their own country? Who is to be preferred? American idealism or Fowler's cynicism? And who is to be morally condemned? These are not easy questions and anyone who says they have a complete answer is lying.
Whatever your answers, Greene was very prescient about how American foreign policy would develop in the decades to come - the pursuit of idealistic and laudable goals with practices that in the minds of many fell short. Idealism through realpolitik, you might say. I need not remind you of the relevance of such questions, and hence Greene's book, today.
1. The history of conspiracy theories is remarkable, and we would understand the twentieth century much better if we understood them completely. Look how popular the anti-American conspiracy theory is today; and I'm not even especially looking at the left wing (as if they were exclusive to that wing), but more at the Third World. Hugo Chavez, whatever you may think of him, is a prime example. The most stupendous believer was Stalin, who believed in a huge Anglo-American conspiracy that was tearing down Russia (when in fact he himself was doing it, this being the 1930s) at a time when British intelligence had thirty employees and there was no American intelligence service.