The following AskReddit thread reveals how people found out they were asexual.
Source list available at the end.
1. "Off" Feelings
I always felt sort of "off" about my feelings towards girls growing up. For some reason, it never really seemed to click for me. In high school, I remember a bunch of my friends talking about an erotic movie, and I was just kind of nodding and going along with it. After some reflection on the matter, I realized that I wasn't actually interested in erotic movies and sort of left it there. Didn't think much of it because I was still interested in girls, but it was super common, and I was awkward enough that I'd never bothered acting on it.
Fast forward to the first-year of university, and I started realizing that while I was attracted to girls, it was more romantic. I just wasn't interested in sex. One night, I was really drunk and just feeling down. I eventually asked my best friend when he first started feeling sexual attraction and he told me grade 7. Just like that, it really hit me, and I felt really weird for a while.
So, how does it affect me today? Well, it's been about 3 years and most of my close friends are aware. The response is usually either "What?" or "Cool." Nobody's been particularly negative about it, and I don't really worry about it. I'm still not in a relationship, but I'm not exactly in a hurry to get into one since I have no idea how I'd even react to the situation. I don't think I'd ever do it with someone who wasn't asexual, but who knows.
2. That Sounds Like Me
I don't think you really discover you're asexual in the same way as you discover you're gay/straight/whatever else you may be. Like you don't have a moment in puberty where you go, "I'm not sexually attracted to anyone!" It's more of a gradual realization that other people are experiencing things that you're not quite getting, and your friends start talking more and more about stuff that really just doesn't seem to interest you in the slightest.
In my case, and in the cases of many other aces I've spoken to, over the years, it led to feeling like there was something wrong with me, and that I was somehow broken or abnormal. It can take a long time to get away from that mindset.
I never considered looking it up because I just thought I was weird and broken. It wasn't until I was befriended by another asexual, who was open and confident about their sexuality, that I kind of went, "Oh, that sounds like me." I then looked further into it.
Basically, I have never looked at someone and thought, "I want to have sex with you." No one has ever been sexually appealing to me, and the whole idea of sex is just a big no. Not everyone who is asexual is against sex though, being asexual just means you are not sexually attracted to any gender. Plenty of asexuals have sex - some just for the physical feeling, some to satisfy their partners, etc.
3. Never Interested In The Same Way
I was always led to believe I was asexual by my friends in high school because I was never attracted to, had relations with, or interested in boys the same way they were. They would tell me how they'd want to do things sexually with certain people and such. Whereas, I would just fantasize about holding hands with them. I find many men attractive, but not sexually. How handsome I find a man often changes with how smart or nice they are, and other people don't seem to have this dichotomy in assessing someone's attractiveness. I have yet to develop a romantic or sexual relationship or even relations with anybody, I know right, I'm just attributing everything to being a "late bloomer."
4. Abnormal is Normal
I thought I was a late bloomer, and then I thought, "I'll want to have sex when I'm with the right person and feel ready," Then, when I was over 18, I started thinking that if anything was going to change it should have happened already because I still had no interest in sex and still was not attracted to anyone sexually. When I was nearing 20, I was thinking there was something fundamentally wrong with me. And then, I found out about asexuality and things kind of clicked and made sense. I felt less alone and broken.
Don't get me wrong, I still sometimes feel like I'm broken somehow because of it, or like I'll never have a happy relationship, etc. I think everyone gets insecure like that at times. Overall, I'm much more happy and confident in my sexuality knowing I'm asexual than I ever was thinking I was just abnormal.