Finding out who you are is something everyone deals with in a different way. Some people slowly get to know themselves through how they handle situations and events in their lives, and some people determine who they are and who they want to be quickly, and don't stray far from that throughout their lives. All of the things in your life combine to make up you who you are. Who your friends are, the music you listen to, the clothes you wear, how you choose to spend your free time, your chosen job or career... but there are layers beneath the surface, and the every day routine that make you unique.
Although some people may think it comical, the concept of not really knowing yourself is a common obstacle, especially for teens, and young adults. The best way to go about truly finding yourself, is by diving inward, and not allowing other people to decide for you.
Some ideas on how to start the process may be just doing simple things like exploring different types of music, trying out different hobbies or sports, taking some local classes or workshops, spending time with new groups of people, trying out new recipes or restaurants, and just determining likes and dislikes. Once you have a basis, it will be much easier to figure out the rest.
Another idea might be to check out the internet, or local newspaper, and educate yourself on local and world events. By determining your stance on more serious issues such as GLBT rights, abortion, abstinence, religion, politics, animal rights, etc., you start to develop a deeper sense of those underlying layers, that seperate you from your peers.
Traveling is also a great way to get to know yourself pretty fast. Being outside of your regular element and comfort zone, and facing new things on your own can really help you determine how you'll handle yourself throughout your life, and who you want to be.
Although all of these things will help you develop a more complete idea of who you are on the surface, the deep, internal characteristics cannot be determined in a weekend, or a month. Some things just require time, and life experience. That can be the best part... knowing everything and living your life as a pre-packaged, perfect person would be boring! Living your life, and learning as you go is what makes you who you truly are. The journey is the best part! So don't be in such a hurry to figure everything out, but get excited to try new things, and to learn new lessons.