A molehill is the same shape as a mountain, just very small in comparison.
So if someone reacts to a situation in a MUCH worse way than would be expected, they're, "Making a mountain out of a molehill.".
Like, "my boyfriend told me he can't come out with me this Saturday, he said he has too much work to do" - the normal reaction would be, "oh that's a shame, but at least he's getting more money and he will be popular with his boss" -
Making a mountain out of a molehill, the reaction would be something like, "HE'S CHEATING ON ME!! I CAN'T BELIEVE IT!! ALL MEN ARE B*STA**DS!!! I KNEW SOMETHING WAS WRONG!! WHY DOES THIS ALWAYS HAPPEN TO ME? I'M GOING TO DIE I CAN'T TAKE IT!!".
Reacting to a small issue as though it was a huge issue - and sometimes for the attention.
I know someone like that, she, "always makes a drama out of everything".