You described the classical monetary policy tool: Open market operation in this example. They also have other tools like Required reserves and Discount loans but the simple monetary policy theory which boils down to the money supply manipulation causing the interest rates to change cannot quite well explain the FED direct intervention in the market targeting the interest rates.
By increasing money supply, the vertical line shifts to the right dropping the interest rates:
When interest rates drop, it becomes more profitable (and affordable) for customers to take out loans and increase consumption. As a result, the aggregate demand curve shifts to the right surpassing the equilibrium which increases the overall price level in the country referred to as INFLATION. When money supply decreases (not surprisingly) vise occurs.
So the ultimate path is such: increasing the money supply causes inflation. But money suppy is not the only variable affecting the price level. Suppose the outbreak of fighting in some unstable country causes investors to become pessimistic about the future profitability of investment in the area and pull their money out decreasing the investments as a part of GDP. This causes the short run aggregate supply curve to shift to the left also increasing the price level. But in the long run, demands also fall in response since high prices cause aggregate demand to decrease (people cannot afford those prices) and the new equilibrium is found.
Having that said, no matter which tool FED implements to increase or decrease money supply in the economy (open market purchases, RR or discount loans), targeting interest rates became evident when FED chairman - Alan Greenspan informed congress in 1993 (if I remember correctly) that FED would cease using M1 and M2 to guide the conduct of monetary policy and put their emphasize on interest rates.