Start the story with an event. Try to avoid the obvious, "I was born on a cold, dark night . . ." approach. Your autobiography should include information about where you were born and your upbringing, but that doesn't necessarily need to be where it begins. In fact, in most cases it's the best place not to begin.
Start with a hook. An autobiography is not fiction, but the same rules of good fiction writing apply when it comes to starting your autobiography. You need to hook readers in the first couple of pages. You care about the story because it's your life. Don't assume readers care. You need to give them a reason to want to read your story. Start with an event. It might be something tragic, it might be something you've accomplished that changed the world. Whatever it is, start with that event first, then you can go back and give a little of your history.
Don't begin your story with details about your life that will not move your main story forward. Just because you're writing an autobiography, that doesn't mean every single aspect of your life story needs to be included. You're writing with a focus. Everybody has a life story. Why is yours important enough to write about? Include the details of your life that contribute to the focus of the story.
Try to sum up the tone of your book by the end of the first chapter and remain true to that tone throughout. You're introducing yourself to readers and you're about to share intimate details of your life with them. Let them know by the tone you set who you are and who they can expect to be spending time with. If you have a story to tell and follow these guidelines, you'll hook readers and make them care about what you have to say.