As you say, the Fed has three main tools that it can use to affect the supply of money in the US economy. These are the required reserve ratio, the discount (interest) rate, and open market operations.
- Required reserve ratio. When banks take in deposits, they are required to keep a certain percentage of those deposits as reserves. The remainder can be loaned out. The more that the banks can loan out, the greater the supply of money. This is the least commonly used tool of monetary policy.
- Discount rate. The Fed lends money to banks for short terms. It sets the interest rates on that money. The interest rate that it sets generally influences the interest rate that banks charge when they loan money out. When the Fed decreases interest rates, more borrowing tends to happen because borrowing is less expensive. This increases the money supply.
- Open market operations. This is the term for the Fed buying and selling government securities from banks. When it buys securities, it gives the banks money in return for the securities (which were not liquid) that the banks held. This increases the supply of money in the economy.
Through these three tools, the Fed conducts monetary policy for the US.