The Structure of the Fed
The Federal Reserve was created by Congress almost 100 years ago, when the economy and markets were very different from today. Creating a central bank was controversial at the time and the political compromises led to a peculiar structure (see here for the official version of the Fed’s history; there are numerous alternate versions of the Fed’s history, including this one that is considerably more skeptical).
The Fed consists of 12 regional Federal Reserves that were established in the large financial centers of 1913; there is only one regional Fed in the western US (in San Francisco) while there are two in Missouri (St. Louis and Kansas City). You can see the map here.
The decision making body of the Fed is the Federal Open Market Committee (FOMC). When you hear that the Fed cut rates it is by a vote of the FOMC. There are two sorts of members of the FOMC: seven governors, selected by the President, who serve 14-year terms. Due to a conflict between the Democratic Congress and a Republican President there are currently several vacancies; Board members can remain on the Board until their replacements are named or until their full 14-year term is completed. Few board members serve a 14-year term, so a two-term President is likely to have the opportunity to name all seven Board members.
The remaining five members of the committee come from the 12 Presidents of the regional Federal Reserve Banks (on a rotating basis), who are selected by the locally-based Directors of the Banks (see here, at the bottom of the page, for the list of which Fed President serves when).
The crucial policymaking is done at meetings of the FOMC in a large conference room in the Eccles Building in Washington, DC. Sitting at the table are the Chairman of the Fed (Ben Bernanke), the Vice Chairman of the Fed (Donald Kohn), the other five governors, the President of the New York Fed (Timothy Geithner), who is somewhat confusingly the Vice Chairman of the FOMC, and the other eleven regional Fed Presidents, four of whom are voting members of the committee at any time (the other seven participate in the discussion but do not vote). Also in the room are a number of high-level Board and regional Fed officials and economists who make presentations to the committee on various topics.
Recent Fed Chairmen (Bernanke, Greenspan and Volcker) have had a very important influence in Committee decision making. While there may be extensive debate on what the Fed should be doing, there are very few close votes. It has been said that three negative votes are sufficient to veto any policy decision, so in recent years most votes have been unanimous or with one or two members dissenting.