Open with a vivid image. Sometimes visualizing yourself as already having accomplished your goal will help you to accomplish it. But writing the description of how you would look upon reaching your goal may not only help you to achieve it, the description will engage others. For example, you might say, "I picture myself on a fair day with blues skies, having just swung my nine iron. My body still in its follow-through posture, I am watching the ball sail through the air until it arcs back toward the earth and finally, wonderfully plunks into the white cup in the ground. It's a hole in one. My goal accomplished."
Begin, alternatively, with a biographical note about yourself, one that illustrates why your goal is important to you and how it will fill a need in your life. Keep it short, preferably only one or two paragraphs long. Tell the story of how you discovered this need in your life or how you found out that you are driven to accomplish one thing more than anything else. If possible, incorporate sensory impressions to make the opening more compelling.
Get right to the point. Tell the reader what your goal is in the first sentence. The sentence might be an opening paragraph all by itself. You may also use this technique in conjunction with one of the other two methods. It will work best if you have an unusual or startling goal. To say, "I want to be a millionaire" is too common. But maybe you want to write an outstanding book, and your hallmark of literary success is a little quirkier than most people's. It's not the Pulitzer you want, but an interview with a famous radio personality. You might write, "Someday, more than anything else, I hope that Teri Gross calls me up and begs to interview me because I have written the most sensational book she's ever read. That's when I'll know I have made it."