Brief Summary
The Set-Up
The minute World War II ended, the Soviet Union stopped playing nice and took control of several Eastern European countries. By 1947, Soviet expansion had gotten way out of hand, the British were pulling troops and supplies from the Middle East, and the U.S. needed a revised direction in foreign policy to assert its global position in a new Cold War.
The Text
Truman makes the case for his foreign policy recommendation by describing the civil war between communist and anti-communist factions in Greece. Then he describes the developing threat of a communist insurgency in Turkey. If just one of these countries is lost to communism, he says, then other countries in the Middle East will follow (like a line of dominoes) until the entire region is donezo. This will affect the West just as much as it will affect the East, and seriously might happen, considering the British are about to dip from the Middle East.
Along the way, Truman takes some jabs at the Soviet Union (without ever mentioning them by name), brings up WWII, and uses a lot of patriotic and democratic language to suggest that it is up to the U.S. to save both itself and the rest of the world from the Soviet threat.
The speech ends with an official declaration of foreign policy that says the U.S. will provide military and economic support to countries fighting totalitarian—a.k.a. communist—forces. Oh, and he says that we need to get on all of this ASAP.
TL;DR
Harry S Truman, one of our sassiest presidents to date, took the U.S.'s stance against communism from "not in my house" to "not in anyone's house."