Begin your first paragraph with a sentence that cuts to the heart of the piece's main action or conflict. For example, if you are writing a story about a man who drowned in a lake, you might begin with, "Jim's boat was found after he'd already been missing for two days." If you are writing an opinion or critical piece, you might begin with, "The national deficit is at its highest in over 100 years," which quickly and dynamically cuts to the central issue. This will hook your reader and make him want to read further.
Begin with a short, declarative and arresting sentence rather than a long, meandering one. Tell your reader precisely what this story or essay involves. For example, if you are writing about the dying art of letter writing, you might write as a first sentence, "No one buys stationery anymore," and follow it up with what people buy instead. Beginning with this sort of pithy statement helps create your personality as a writer and entices your reader to listen to your point of view.
Begin with an unusual or extraordinary description of the thing, event or issue you will discuss in your piece. Make your description slightly mysterious, providing some of the information but not enough for your reader to fully understand the situation or thing being described. Think of the opening passage of Faulkner's "The Sound and the Fury," for example. Describing something in a way that leaves your reader guessing will make her want to keep reading to figure it out.
Involve your reader from the beginning by addressing him directly, using the second person singular. A reader who is involved in the situation or issue is more likely to feel personally invested in the writing, even if the scenario is far-fetched. For example, you could begin, "You don't want to be a child anymore, but you don't want to fully grow up; you want the freedom of the open road without the responsibilities that that freedom involves..." This way, the reader can identify more easily with the piece.