"How come...?" is a politer way of saying "Why...?", except it refers to a situational outcome. If you don't want to sound nosy, you can use "How come...?"
What happened to Sarah?/She lost her job./How come?
God, I'm so depressed./How come?
How come you're saving all this money?/Because I need a new car.
You wouldn't use it if it's not rude to want to know the answer. "Why is my house on fire?!"/"Why am I missing $300 from my bank account?!"
or if you're being a bit rude/cheeky/casual "ARGH! I failed my test! Why am I so dumb?! Why?!"
You would use "How come...?" at work when talking to colleagues and bosses and to strangers you want to be polite to (to customers, you say "May I ask why...?"). And you would use "Why...?" most any other time.