What exactly is Ousama Game in this titular series? How does it work?
The Wikipedia article on Konpa (which are basically alcohol-fueled "get to know each other" events) describes it. Basically, the rules are:


Everyone gets a piece of paper which either has a number on it, or identifies them as the king.
The King reveals themselves.
The King issues a decree/dare, including some of the numbers (for example "Number 2 has to kiss number 3's index finger").
The people whose numbers match the decree reveal themselves and do the dare.


It's a bit like a semi-anonymous version of Truth or Dare.