There is a lot of hub-bub out there about "finding yourself." Authors claim to have the secret to helping you find the you inside of you and offer up advice on how to stay true to yourself. While I'm sure some of these authors may actually have sound thoughts on the matter, I am of the belief that a lot of this is unneccesary attention to the self.
What I mean is that we can get so caught up in finding ourself that we do it at the detriment of others. It can accurately be given the title of a selfish pursuit.
With that out of the way, if it made any sense, I think the best way to discover who you are is to try lots and lots of things. Things that you would not ordinarily do; things that are out of your comfort zone; things that other people will look down on you for. Then, review what you have accomplished and failed at and focus on what you enjoyed the most. Get rid of the crap that is clutter in your life, and then just focus on the things that you enjoy.
Now, there will be things in your life that are a part of you, your personality, and can almost be kept around with the excuse of, "it's just who I am." Bull crap. If you have a problem with lying, deal with it. If you have a problem with gossiping, deal with it. Jealousy? Deal with it. Etc. Read Philippians 4:8.
Personally, staying true to myself means knowing who I am (which I believe will be a life long journey of constant readjustment) and not allowing anything to change who I am, unless the change is for the better. Staying true to myself is knowing myself.
Honestly, the part of me that I think about the most is "what am I going to be?" As I male this is probably considered a natural question to ask and harp on, but I must say that it is getting old. Within the past year I have definitely focused on what I want to do (which as a guy makes up a lot of how I think of myself). Specifically I want to teach the Bible. The next part of this question is where do I do this. And this is the part of myself that is not up to me, but is up to God. My passion for teaching His Word is ultimately in His hands to point me in the direction to go.
(A negative part of me is impatience with things like this, so waiting is hard :-) )