Who actually decides how much money exists?

No single person decides. The money supply comes out of a constant back-and-forth between central banks, commercial banks and the rest of us, and the surprise is who does most of the creating: your ordinary bank. Whenever a commercial bank makes a loan, it simply creates a matching deposit in the borrower's account. That new deposit is new money. When the loan is repaid, the money is destroyed again. This is why bank deposits make up by far the largest part of the money supply, while banknotes and coins from the central bank are only a small slice.

If money that exists only as a number in a computer sounds flimsy, consider the Yap islands in Micronesia, where people treasured huge carved stone disks. Ownership of a big stone was settled by its story, told and retold, not by where it stood. One stone once sank to the bottom of the sea during transport. Nobody ever saw it again, yet everyone agreed it was still there, so it went on being traded like any other. Money works because we all agree it does.

So where does the central bank fit in? It sets the stage. By buying or selling government securities and, above all, by setting interest rates, it makes borrowing cheaper or dearer, and so influences how much new money banks create. Its main goal is price stability, because a money supply that grows too fast is tightly linked to inflation, which erodes real wages and the purchasing power of every coin in your pocket.