Well - theres the suicide attack...
you attack with the DF and your opponent blocks with their 1/1, so both would die... once damage is on the stack - you sac him to get your land... still killing the opponent's creature.
In response to spells or abilities - it works pretty much the same way... if you have to target a creature only on playing the spell, you can sac the DF once the spell is on the stack and get your land without countering the spell or ability...
