OP, ask yourself what you truly desire. You crave closeness? An authentic relationship? Someone to be at ease with, someone you can be yourself with? Perhaps there's
this one girl you know always in your mind?
From the way you worded your post, it sounds like you are feeling left out from human interactions that look so easy and natural for everybody but you,.. and sorry to be blunt, but that's only an illusion, a painful one at that, but still an illusion.
Don't be ashamed if you want 'just a relationship, any relationship', that doesn't make you shallow, just curious. As long as you and your eventual mate respect each others' will, agency and sense of autonomy.
There is no guidebook, there is no "girl code". We're all human beings, all afraid of rejection and manipulation and loneliness. When people talk about special signals and codes mean conventions that only a handful care about, and will count jack shit when you're truly close to someone.
Gender roles in the heterosexual dating scene in our societies (i take it that you're from a western country, correct me if i'm wrong) puts lots of pressure on males to initiate, hence from male point of view rejection feels like the main problem. From female point of view there's pressure to be the social one in the couple, keep things going
no matter what, etc. which is just as crushing, but i digress.
Reaching out is painful at first, especially if you are a fellow introverted, but you'll develop your unique stile suited to you.. only by interacting.
Take baby steps. Go out of your comfort zone at your own pace. You are the only one that can do it and knows how to do it. While it's tempting to follow advices, because you feel that being yourself is right what made you lonely in first place, advices are void and outright dangerous if you don't dissect them first and adapt them to your unique personality. If some approach doesn't feel natural to you, don't force yourself to blurb out things you'd never say on your own. It will only make things worse for everybody.
Consider: you have nothing to lose AND you have nothing to win.
Meet new people. Talk to girls as you would talk to any other human being. Share your interests, share experiences together. They want to have fun just like you, muse about things, enjoy understanding and care.. just like anybody else.
The point of all of this is not just getting to know a possible partner, the point is getting to know -yourself-. Only then you'll be able to face and accept possible rejection and move on. And at that point you'll be to busy enjoying your life to worry about when your time will come, because you will be already living it without realizing.
Oh, and personality TRUMPS good looks. Hard.
It becomes much more evident toward the 30s, i guarantee you.
By personality i mean of course the sincere sharing of one's mind and soul, not that PUA/social engineering bs.
"Friendzoning" is a ridiculous concept perpetrated by manipulative assholes. Many a "nice guy" do this, trying to be nice and everything to gain affection, and get upset when the girl they're trying to woo isn't into them for whatever reason. They mistakingly assume it's because they're a friend, not a lover.
The reality is, if a girl just wants to be friends, that's because she wants to be friends. You are not her type. Period. And assuming you're NOT a manipulative ass, and are actually being nice because that's who you are, you won't get upset over this. You just got a friend; you should be happy. If you ARE a manipulative ass and are being nice solely so you can get in her pants, then fuck you. You don't deserve her.
At the end of the day, all you need to do is be up front about what you want and your intentions. Don't try to "play your cards right." Don't recite pickup lines. Be yourself, communicate what you want, and if she reciprocates, you've got yourself a girlfriend. The more you try to woo her, the deeper a hole you dig. Stop wooing. Stop manipulating. It's not a game, where you can "win." If you're being nice to a girl, it's because you want to be nice to her, not so you can make a good impression or somesuch bullshit. Put yourself out there, and not some mask you wear, and you'll eventually find a girl that's into you, and not some character you pretend to be to try and be more attractive.
This. So much this.
Edit: forgot one thing.