How Money Circulates
The Treasury Department ships new paper money and coins to the Federal Reserve Banks; the Reserve Banks pay it out to commercial banks, savings and loan associations, and other depository institutions. Customers of these institutions withdraw cash as they need it. Once people spend their cash at department stores, grocery stores, and so on, most of this money is eventually redeposited in depository institutions. As notes wear out or become dirty or damaged, depository institutions redeposit them at the Reserve Banks.
Well, it's all kinda there to begin with. To simply extremely, on day one a bank starts up and says "give me your savings, and I'll grow it for you" You bring in your money, and the banks says "I've got money to lend if you pay me interest" Then the bank makes sure it charges more interest to the lender than it pays the investor, so it covers it's costs and makes a profit. The mint usually only ever swaps money, never injects new money to a system.