Combatting inflation and combatting unemployment are two opposite tasks. Monetary policy tools are used in opposite ways to combat these two economic problems.
When there is too much inflation, it generally means that the economy is “overheated.” There is often too much demand so prices start to rise at relatively high rates. At times like this, what the Federal Reserve (which controls monetary policy in the US) wants to do is to reduce the supply of money. When the Fed does this, there is less money to drive demand and prices should fall. The Fed can do this by requiring banks to hold more reserves and therefore loan out less money. The Fed can raise interest rates, thus making it harder to borrow. Finally, it can sell government bonds, thus taking money away from banks and out of circulation. All of these things reduce the money supply and, thereby, reduce aggregate demand.
When there is too much unemployment, it generally means that aggregate demand is too low. At times like this, the Fed wants to put more money into the economy. Therefore, it does the opposite of all the things mentioned above. It lowers reserve requirements and interest rates and it buys government bonds. With more money being pumped into the economy, demand should rise and unemployment should fall.