Openings of stories need to do three things.
1. Start the story moving - this means showing the reader what kind of story this is to be.
2. Introduce and show what the main character is about, who they are and what they want.
2. Engage the reader - This means making a promise that this story will be a good one.
There are a few extras like establishing the tone or mood of the story, perhaps showing a viewpoint character who isn't the hero or heroine but an observer, and perhaps throwing in a minor character or two who have a role in the story -- not too many for this becomes a mob scene.
How does a writer do these things? Talking here about the first 3 to 5 pages of a book/
1. Open with a scene - this is the easiest to do since it can show the main character or characters in action, give a hint of the setting. Things to avoid are long descriptive passages, huge sections of back story or opening with a bang that becomes a promise not kept during the rest of the book. This kind of opening can work for an action story.
2. Open with dialogue but before long one must add other elements.
3. Open with description - must be a masterful. 3 to 5 pages of description could bore the reader.
4. Start with a philosophical statement - As long as this doesn't go on for pages. Too much and it becomes preaching.
Remember the opening of a book is a promise of a good read and to do this revision is the way to go. Finish the book and then go back and revise. The opening may need to be changed and that's all right. Revision can be as much fun as getting the initial story down.
3. Open with Description - takes a master and