Econbrowser has a lengthy, wonkish post that endeavors to explain how the Fed works, interacts with the Treasury, and is struggling to provide responses to the credit crisis without triggering inflation. Even this simplified description is complex, which illustrates the difficulty of the situation.
Thus far, it appears that the stimulus packages are operating as designed and are not inflationary. In fact, deflation continues to be a real threat, so much so that economists are calling for slightly more inflationary policies. On the other hand, Bernanke is operating in uncharted waters and high inflation is not entirely out of the question:
The bottom line is that Bernanke has made a gamble with something approaching 2 trillion. If the gamble wins, taxpayers owe nothing. If the gamble loses, taxpayers are committed to borrow a sum equal to any losses and start making interest payments on it.