The easiest way to get alcohol during Prohibition was actually legal.  This was by way of prescriptions.  A doctor would be paid a set amount of money to prescribe a certain amount of liquor a day.  The doctor’s signature became extremely valuable and sometimes gang wars were fought over who owned what doctor.  Forgery was also common and gangsters often stole stacks of blank prescriptions.  These would also be on sale in a speakeasy. 

Here is an example of a prescription for whisky from 1924:

Here is a prescription for "Spirits Frumenti," the medical name for alcohol.