The process of a contractionary monetary policy involves reducing the money supply. The reduced money supply then leads to a reduction in the rate at which aggregate demand is increasing. As aggregate demand starts to increase more slowly, the price level also increases more slowly. This reduction in inflation is the point of a contractionary monetary policy.
There are three tools the Fed can use to introduce a contractionary monetary policy. It can raise the required reserve ratio for banks. It can raise interest rates. Finally, it can sell government securities to banks. In each of these cases, what happens is that less borrowing and lending is likely to occur. If banks hold more of their deposits, less is lent. If interest rates increase, borrowing decreases. If the government sells securities, banks’ money goes to buy the securities instead of being lent.
If less money is lent, less money will be spent. It will be harder for consumers to borrow to buy “big ticket” items. It will be harder for businesses to spend on new equipment. Both of these trends will lead to a reduction in the growth of aggregate demand. This will make inflation slow down.