What are the major goals that the Fed has to achieve through managing the nation's money supply?
The main job of the Federal Reserve is to manage the US's monetary policy. This means that they do things like manipulating interest rates and buying and selling government securities so as to keep the money supply at the right level.
The Fed tries to accomplish two things. It tries to make sure that the money supply is not too high because that would cause inflation. Conversely, they have to make sure the money supply is not too low because that would prevent the economy from growing at a good rate.
So, the Fed is trying to keep inflation low while still maintaining the money supply at a level that will allow the economy to grow.