How does money actually get into circulation? How does the amount of money in an economy change?
Okay well the first issue I found in your analogy is the idea that printing money decreases its value. This is not true, the value of an individual nations currency is based on many things including the trade between other countries and the currency market. And to answer how the money supply changes( the amount of money actually circulating), it is regulated by the federal reserve board and carried out by each regions federal reserve bank. So, when the fed decides to increase the money supply they tell the banks to buy treasury bills(or T-bills) that are already circulating in the investment sector. They buy T-bills in exchange for cash just like everything else thus increasing the money supply. When the money supply needs to be constrained they simply sell the T-bills they have and keep the money received so that it is no longer circulating.