When I did economics at high school, the liquidity of the Australian banking system was controlled by the Reserve Bank via a Statutory Reserve Deposit Ratio. This meant that a portion of every dollar deposited into a bank account had to be held in reserve and could not be lent out.
For example, if the SRD ratio was 33%, then the bank would be able to lend 67c out of every dollar deposited. This 67c would then be returned to the banking system via ordinary economic activity, and 45c of this 67c (= 67 x 0.67) could then be relent, and so on. If this cycle repeats enough times, then that $1 of liquidity is multiplied by 3. So that's how the banking system of those days created $3 out of $1. I have no idea how it works today.