I began identifying with the female gender, and identifying more with girls, pretty much as early as about 2nd grade. Although I was NOT consciously aware of this at the time. I had no reason at the time to doubt that I was anything but a normal boy, and it's only by looking back that I can really realize "oh yeah, so that's why I was acting this way."
I first became consciously aware that I was identifying more with the female gender, and was actually kind of jealous of them, around age 13.
Official gender dysphoria, where I actually started hating my body and consciously wishing that I could be a girl, started around age 14-15, at about the same time as my voice started changing, I started growing body hair everywhere, and a certain lower member started getting bigger.
The first time I really realized that it was possible that the label "transsexual" was what I was feeling, that also came around age 15 or so. Although at the time, despite how strong my feelings of dysphoria were, and despite how much I wished I could be female, I refused to apply that label to myself due to misinformation about what being transsexual meant.
After two years of gender dysphoria nearly completely consuming me, and interfering with just about every single facet of my very livelihood, I converted to Christianity at age 17. At that point, I started viewing my gender-related desires as sinful, and something that I had to just get over, and started to try just being happy as a guy. For the next 10 years, I suppressed it with varying degrees of success. It was easier to ignore during the happier periods of my life, specifically when I fell in love for the first time, but the feelings of gender dysphoria, and that identification that I had with the female gender, NEVER went away, despite how many times I tried to "rebuke Satan" to make them stop, and despite how much I told myself "just be happy as a guy. It's what God gave you. Embrace it!"
At age 26, after an entire college career of never living up to my full potential, I decided "all right, fine, if I want to express these feminine desires, who says that I can't? Let's go back to wearing short shorts, and shaving my legs, and doing all of the things that I've always wished I could do. Who says that I have to be a girl in order to do those things?" So I started dressing again, and started doing the feminine things I always wished I could do, like shaving my legs and acting more effeminate. And, well, even then, it still didn't work. I still felt like someone that I wasn't... a guy trying to act like a girl. It wasn't enough. I still wanted to actually be a girl. And I was still jealous every single time I saw a woman.
At age 27, I officially accepted that I was transsexual. I realized that nothing I was ever going to be able to do as a guy was ever going to cure my dysphoria, and that the only solution was to transition. I started HRT almost immediately, and I seriously could not be happier with my decision. The only thing left that's bothering me is how damned long HRT is taking. But at the same time, for the first time in my entire life, the dysphoria is easing. For the first time, I'm actually starting to feel comfortable with who I am, and feeling able to truly express myself, and feel like my mind is actually working in the way it should be.
I don't think the reality of it, and the true "coming to terms with it," though, started until I got my official lab results back about 3 months into HRT which said that I really was 100% hormonally female... that my T levels and E levels were now no different from that of a genetic female. That moment just blew my mind, and really made me start realizing that I was a woman... not just a guy who wanted to be a girl anymore, but really, truly, female. And it's an ongoing process as I explore this new self and truly do come to terms with the fact that my future is now as a woman, and I really am going to grow up to have boobs and hips and wearing dresses, not just in some mental fantasy-land, but actually in real life! I love it!

This is just one girl's experience of course, but yeah, that's what it was like for me.