A campaign is a shared story. The premise of the fiction is determined by the DM, and the page-to-page action is determined by the player characters. Like all good fiction, a good D&D campaign should strive, at every turn, to move the story forward in much the same manner as a short story or novel.
Novels usually begin one of two ways: a prologue introduces a primary character at a dramatic point, or the story begins in the middle of an event. Unless a gaming group is keen to role-play their characters' backgrounds--which should already be in place when the game starts--the campaign should start in the middle of things.
I know I am taking a divergent tone here, but the staple campaign begins in an inn or tavern. While such an introduction eases players into the story, it is grounded in the facade of choice. The town's mayor will invariably ask the players for assistance, or the hooded-and-cloaked wizard will offer a substantial reward for the players' time and effort. Rather than open a campaign with a vague sense of direction, I choose to start a campaign with an event already in motion. The players return from a month-long journey to find their home town under attack, or perhaps the players awake in the middle of the night to the sound of steel clashing with steel as city guards try to find off a dastardly kidnapping perpetrated by cavalier bandits. The event occurs, and the players have a choice: do they involve themselves in the situation, or do they sit back and watch? Either choice can lead to a furtherance of the story.
Generally speaking, I usually have two to four linked stories in one campaign. As the players resolve one issue, they discover a hidden depth to the story that leads them toward a new problem. I provide the overarching story--the end-goal of each segment of the campaign--and I leave the players to their creative approaches when they try to resolve the problem. NPCs might provide assistance in the form of advice or maps, but such assistance must be sought; it is never freely offered. Also, the interim points of an adventure--the time spent traveling, the nightly rests, and the passage through a city or town--don't always need to be fully explored; if nothing important happens, a brief explanation of the setting and background activity should suffice. When something important occurs, time can slow down to its normal crawl, and the players can immerse themselves in a given situation.
What does this storytelling approach accomplish? It tells a clear story that always provides a sense of direction. It gives players the ability to measure their progress. And it allows for a measure of freedom and choice that never feels like a random choice made by an unprepared DM.
The start of a campaign--the first hour, the first encounter, or the first session--can determine the players' general outlook for the rest of the campaign. If a DM can set a strong plot hook early in the campaign, the entire group has a much better chance to fully enjoy the story that will unfold week by week.