Madness was originally a fairly complex series of triggers so that
   the spell could be cast using the system of priority.  Since then,
   other cards have been created that allow a spell to be cast when
   no player has priority.  This created the opportunity to "clean up"
   the madness rules.  So, whereas before it was possible under some
   circumstances to play a land inbetween the discard of the card and
   casting the card for its madness cost, these days it's much simpler:

   - playing or resolving a spell or ability, or dealing with the discard
   to maximum hand size at cleanup, causes you to discard a card.

   - the madness ability on the card allows you to replace the card going
   to the graveyard with removing it from the game.  Doing so triggers
   an ability: "you may cast this card for its madness cost. If you don't,
   put it into your graveyard."  Since the madness ability retains the
   term 'discard' for this new event, it also triggers anything that
   triggers on a discard.

   - when a player would next get priority, the triggered ability goes on
   the stack.  When it resolves, you choose whether to cast the removed
   card or not.  If so, its cost will be the madness cost instead of the
   mana cost.  If not, it's put into your graveyard.