"It was a dark and stormy night."
Other than being a horrible cliche, this classic, terrible story opener fails to do the most basic thing an opening line is designed to do: grab the reader. No one wants to read stories about the weather. So how do you grab the reader in one line?
Humans are social creatures. We are naturally curious about other people--even fictional ones. As such, an opening line about a person in a sympathetic situation should do the trick. Imagine a story that starts out...
"Claire was running out of time. She squeezed at the small puncture on her arm. Her vision blurred as she peered around the corner in the dark alley. The silhouette of a man stood between her and freedom."
The first sentence gives us both a person to root for and some tension. We, as readers, are conditioned into thinking the first character introduced is generally the protagonist. Therefore, we already know to root for Claire by the end of the first sentence.
What's coursing through her veins? We assume it's poison. Maybe she was drugged or bitten. At this point, it's not explained in detail. Why? Because that's not important right now. What is important is that the protagonist is in trouble, the situation seems desperate, and there's a shadowy figure that serves as an obstacle Claire will need to overcome before time runs out.