The late, lamented Miss Snark (who according to my inside sources has transmogrified into the Query Shark, bless her) had a great summary for a query that included "What happens in the first fifty pages". These days, when the markets are so tight, I recommend to my students that something had better happen in the first ten pages. At the very least, there has to be some sort of tension--an unresolved question, a curious circumstance, the threat of danger--in order to persuade the agent/editor/reader to keep turning pages.
I'm reminded by a recent manuscript, sent to me by an aspiring author, that possibly the most common error for new writers is starting the story in the wrong place. I did it myself, with my first novel. I was having difficulty selling the book. Then, on the advice of a really smart writer, I lopped off the first fifty pages. No one ever missed them! The story started, as I always say now, where the trouble started, and that made all the difference.
This doesn't mean, I hasten to add, that a story should start with an explosion or a murder or other scene of mayhem. If the reader doesn't know the characters yet, the reader won't care if one or more of them die. The writer's job is to give the reader a connection to a character from the very first page, so that when the hook is set, it can't simply be pulled out and tossed away. By the same token, nothing sinks a manuscript faster than an expositional lump right at the beginning. Forget all that backstory--for the moment. It can be worked in later, maybe in dialogue, maybe in memory, maybe just with a remark here and there.
I often recommend to students also that they re-read a favorite book or story, and analyze the opening. How did it hook them? What made it un-put-downable? Years ago I fell in love with the stories of the British writer Rosamund Pilcher. She had a way of making her characters step right off the first page and into my heart. I read every one of her books--they're still on my shelf--and I studied those first pages to try to divine her trick. I couldn't tell you in academic terms exactly what she did, but it seems to me I internalized something from that process, and it's been most helpful.
We all laugh at "It was a dark and stormy night", but really--I'd read a story that began that way, wouldn't you? Something's about to happen. We can feel it. We know that somehow the storminess of the night has bearing on something, and we're curious. Of course, we also know that all nights are dark, except in the Arctic Circle in the summertime, so the line is silly. But we understand that the author knows something is about to happen, and is in charge of this story.
Writers may write openings for themselves, a process the incomparable Madeleine L'Engle called "writing myself into the story". That doesn't mean that those words, deathless prose though they may be, have to stay. "Murder your darlings" is not a literal piece of advice; it means, "Have the courage to cut what doesn't need to be there." Or, as Elmore Leonard said, "Cut out all the boring parts." Especially at the beginning.