Open market operations (in short) are the process of implementing monetary policy. This occurs due to a central bank which controls the short term interest rate and the supply of base money in an economy, and as a result ultimately the total money supply. This involves meeting the demand of base money at the target interest rate by buying and selling government securities.
The Fed conducts open market operations when it buys or sells government bonds. When there is an increased demand for base money the Fed takes the necessary action to increase the base supply of money. In order to increase the money supply the Fed instructs its bond traders in New York to buy back bonds from the public in the bond markets. Because the Fed is paying for these bonds there is an increase in the number of dollars in the economy. Some of this new money is held as currency (the owner literally holds onto the money in their ‘hand’). This means that for every dollar the money supply increases by exactly one dollar. Whereas the new money that is deposited into banks increase the money supply by more than a dollar (for every new dollar) because of the money multiplier effect. The money multiplier is the amount of money the banking system generates with each dollar of reserves. Therefore the fractional reserve banking system is the facet that dramatically increases the money supply.
On the other hand, if the Fed wish’s to reduce the money supply they will sell government bonds to the public through the bond markets. The public pays for these bonds (which goes to the Feds) and thus money is withdrawn from the economy and the money supply is decreased. People will often withdraw money from banks in order to purchase government bonds. Thus the money that is withdrawn leaves the banks with fewer reserves and thus the banks must reduce the amount of money they lend out.
Nowadays most money is in the form of electronic records...