Explain how an open market purchase increases the money supply.
In an open market purchase, what is happening is that the government is buying up bonds that it has previously sold. This is done by the Fed in the United States. This increases the money supply by adding money to the economy in place of a piece of paper that is not liquid.
A bond is an IOU -- it will be worth something at a later point but it cannot be used as cash. It is not really part of the money supply.
When the Fed buys bonds, it gives actual money to investors in exchange for bonds. So if I held bonds and the government paid me $1,000 for them, I now have $1000 more in liquid money than I had a moment ago - the money supply has increased.