The Chairman of the Federal Reserve Board is appointed by the President of the United States. The President gets to nominate a candidate to be the Chairman, but that person does not actually become the Chairman until he or she is confirmed by the Senate. The current Chairman is Ben Bernanke. He was appointed by President George W. Bush. Bernanke took office in February of 2006.
The President may not simply pick whoever he wants to be the Chairman. Instead, he must pick from among the people who are on the Board of Governors of the Fed. There are seven members of this board serving 14 year terms. The president picks one and that person serves a 4 year term as Chairman. He or she can be renominated after the 4 year term ends.