Bad ends in F/SN tend to not be seen coming.
For example, in the first battle against Berserker, how the heck should you know what to do?
Dodge? Run away? I have no idea.
And most especially bad end 13, if I remember it correctly.
It adds to the story such that by not forging a strong bond with your servant, Saber, she becomes lulled in by Kirei's words about the Grail, ultimately killing you in order to get the Grail. Well, she was tricked sooooo.
It mostly happens when you choose the wrong place to go, or the wrong move in a fight. Or if you simply didn't establish a good enough relationship with the characters. That's as far as the bad ends can get in being related to the story.