I belong to pre-modern so I am pretty confused by the rule changes...still had not put my mind to read everything so appreciate the patience...
Suppose I attack with {Ashmouth Hound}. Opponent blocks with a 1/1 and responds by sacrificing to another ability, say {Spawning Pit}.
Question is, will the 1/1 die before he can even respond by sacrificing?
My ans was yes, as the hound has a triggered ability, but wanna know the rules. It sucks being this fundamentally confused.
Whenever a spell or ability is put on the stack, players receive priority in APNAP order and are allowed to cast spells/activate abilities. They are able to sac their creature in response to your hound's damage trigger.
RESOLVED
He can sac a creature after it is declared as a blocker before the damage step. Your creature will still be considered blocked but will take no damage.
If he lets the damage get dealt he can't then sac it after. Once damage is dealt that's it.
Essentially it's all* about the stack now, which you are probably familiar with as the stack is no new thing. In this example, upon declaring blockers, {ashmouth hound}'s damage ability is added to the stack. Priority is passed, as Keyeto explained, and each player will have the chance (in AP-NAP order) to respond to the trigger with any instant-speed effects, which will be added to the stack on top of the Ashmouth Ping. Those effects (including the sacrifice example) resolve first, as the stack clears top-down, allowing this to happen before the 1/1 dies to the hound's effect.
*except for combat damage, which used to use the stack when you played but no longer does :P
Thanks everyone. My brain was essentially fighting over this. Lol.