Comment by otikik

So the simple case is using some sort of state variable:

switch(game_state):

  case(paused):
     <the paused logic goes here>

  case(gameplay)
     <updating entities and regular gameplay goes here>

You still have to be careful about how you implement "gameplay", though. For example if at any point you read the 'system clock' to do time-based stuff like animations or physics, then when you unpause you suddenly will have a couple minutes of advance in a place where you expect fractions of a second.