How did the united states hope to use the policy of containment and the truman doctrine to respond?

The US hoped to stop the spread of communism by these methods.

Explanation/detail:

The Truman Doctrine was first stated by the president to Congress in 1947, saying:  "It must be the policy of the United States to support free people who are resisting attempted subjugation by armed minorities or by outside pressures."  Essentially, the Truman Doctrine pledged American effort elsewhere in the world to check the spread of communist and Soviet influence.  The policy was first put into action in 1948 by providing economic support to Greece and Turkey to stave off communist movement in those countries.  The essence of this policy was called "containment" -- keeping communism where it was and stopping it from spreading.  

The containment policy had been recommended by George F. Kennan, America's ambassador in Moscow after World War II.  In 1946, he sent what became known as "the long telegram" of his advice about what the USA needed to do about the Union of Soviet Socialist Republics (USSR).  Kennan took note of the internal problems the USSR had.  He advised not pushing the conflict too much, but instead just try to "contain" the Soviet Union and wait for their system to collapse under the weight of its own problems.  Kennan was right.  It took almost 50 years, but eventually the communist system in the USSR fell apart.  [The Union of Soviet Socialist Republics came to an end in 1991.]