Controlling the Money Supply
The Federal Reserve has a target rate it hopes to achieve. Although the Fed can dictate rates to banks, it cannot directly control the Federal Funds Rate. The Federal Reserve System tries to control the size of the money supply by conducting open market operations. The Federal Reserve lends or purchases specific types of securities with authorized participants, known as primary dealers, such as the United States Treasury. All open market operations in the United States are conducted by the Open Market Desk at the Federal Reserve Bank of New York. Their goal is to make the federal funds rate as close to the target rate as possible.
The Fed has no idea how many billions of US treasuries it needs to sell or buy in order for the funds rate to reach the Fed's target. It goes by trial and error. That's why it takes a few days for the funds rate to adjust to the new target following an announcement.
Adjustments in the discount rate usually lag behind changes in the funds rate. Once the spread between the two rates gets too large (meaning fat profits for the big banks which routinely borrow from the Fed at the discount rate and lend to smaller banks at the funds rate) the Fed moves to adjust the discount rate accordingly. It usually happens when the spread reaches about 1%.