Board of Governors, appointed by the President and confirmed by the Senate, oversees the Fed's operations.
Monteary policy is set by the Federal Open Market Committee ("FOMC").
FOMC controls the money supply by 1. Open Market Operations (buying and selling securities), 2. setting bank reserve requirements and 3. setting a discount rate for loans to banks or other depository institutions.
The Fed is audited by U.S. government agencies, and its financial statements are audited by an independent "Big 4" accounting firm KPMG.
The current Chair is Janet Yellen. Her predecessor was Ben Bernanke.