Start as close to the end of the narrative as you possibly can. Many listeners/readers have been bored by a-day-like-any-other kind of introduction. Where does the story become abnormal? Begin there.
Hint at or even reveal the climax of the story. If you reveal that your main character will be dead in a skyscraper by the end of the story, then not only will the reader want to find out how your character gets that way, your character's actions will also become more immediately meaningful since the reader can see how each action pushes the character closer to the end. For example, taking an elevator isn't an interesting action in itself, but it can be if you know that the elevator will lead a character to his demise.
Introduce the conflict that is at the heart of the narrative. Conflict allows readers to see what a character is made of and people naturally root for a character that is facing trouble. So show the reader what your character is up against immediately, and your reader will be rooting for the character throughout the rest of the narrative.
Avoid the elements that traditionally make up an academic-style introductory paragraph. Everyone has been writing those three-point essays since grade school so an introduction that utilizes those elements seems cliche. Don't tell a reader what the point (or thesis) of the story is, don't tell a reader how this story will make him feel and don't offer a vague outline (or essay map) of the rest story.
Present as many of the main characters as possible in the introduction. While minor characters can enter and leave stories anywhere, readers like to feel that they know whose story you are telling, and introducing main characters later in the narrative can confuse a reader.