I would start off like this:
Greetings Teachers and Staff at Your High School Name here (staff is for principals and guidance consulars who may read this. Greetings is a unique way of introduction because most students will be using "Dear".)
My name is Your Full Name Here (first, middle, last. If your name is Fredrick but everyone calls you Fred. Write Fredrick with the next sentence being ", known to my friends and family as Fred.) I hope this letter finds you well and that you had a wonderful and memorable summer. The purpose of my letter is to introduce myself and to share my experiences and goals with you, and to give you an understanding of who I am as well as providing an example of my writing skills. (you want to give the purpose in case the letter finds itself in the hands of someone who doesn't know what the purpose of the letter is).
Next paragraph:
The three most important things to know about me are: water-polo, Facebook, and Put something here but not your nephew. Next sentence should be about water-polo: when and how you started playing, why you enjoy it, your achievements, what you're getting out of it from a personal perspective, and if you can fit in something funny here, do that.
Next paragraph:
Facebook. (don't write this part down, I''m telling you this) The issue with Facebook, is that a lot of teachers and adults see it as something which is not useful to students. Young folk tend to spend too much time on it and it's also been used to bully other kids. You want to write something positive here, such as how you've met people from all over the world or how you were able to help a person who was depressed. I don't use Facebook, so I'm not very knowledgeable on how it works. The point is if you're going to use Facebook as a topic make sure it's positive. And it can't be about scheduling water polo events.
Next Paragraph:
Music, if you want to use this as a topic. Describe how music has had a positive effect on you. Here's an example: I began listening to Robin Trower's "Bridge of Sighs", I was curious to know what that meant. I looked it up and learned the Bridge of Sighs is an enclosed bridge in Venice, passing over the Rio de Palazzo. The bridge connects the interrogation rooms to the ancient prisons of Venice. Because of it's structure, the Bridge of Sighs was the last view of Venice prisoners saw before entering the squalor conditions of 17th century Venetian prison life.
That's a long example but it demonstrates that music is something you learn from and not just veg out to. Other examples: Rage Against the Machine, Vietnow, lyric is "Comin' down like bats from stacy coon" it's actually Stacy Koon. Look that up and you'll know what I mean.
You then go into your goals for this year and for your high school years, university and career.
Somewhere you fit in your accomplishments and fit in your personality, your character, your values. but you don't just write: My personality is, or my values are. You demonstrate it with a story.
Lastly, express yourself without using over-used words, for example: I'm curious rather than I'm interested in.
Wow, that was a lot. Apologies for getting carried away. Let me know if you need more assistance.