A lot of people begin autobiographies with how they were born. I always preferred the approach Dickens used in David Copperfield, where the character says he is about to explain whether or not he is the hero of his own life. That approach is more interesting and memorable.
You might also want to check out the free guide on eNotes called, How to write and Introduction.
When you are writing an autobiography as a class assignment, you do not have enough time and space to include every aspect of your life to date. This means that you are probably best off choosing one main idea and purpose to focus on, and the idea and purpose should be stated in the introduction. What events and circumstances in your life have made you the person you are today? These are called "formative" events and circumstances. If your main idea is that some events and circumstances have made you who you are, then your exploration of these will support your main idea and give your essay purpose.
In addition to stating your main idea and purpose, it is always good to give the reader a little "preview" of the topics you will cover. For example, if your formative experiences have made you an outgoing and athletic person, the topics you will want to develop are the experiences that made you this way, and those topics should be mentioned in the introduction.
If you begin with a statement about your personality now, share your purpose of exploration of your "roots" as this person, and offer the reader a preview of how you will develop and support your main idea, you will have a introduction!
A good introduction to any good piece of writing must serve one or both of the following two purposes.
- Give the reader some idea about what kind of information is contained in parts that follow.
- Arouse the interest of the reader in the piece you are writing.
Since you a are writing an autobiography, you are the best person to know what all can be included in it, and what are the most important and interesting parts of your life that you would actually like to include. Once you are clear in your mind about the main contents of the autobiography, you can then think about the ways in which how such contents will be of interest to the readers. Based on this you can write an introduction that aims to meet the two objectives of introduction listed above.