Hey dudes. It's my first post here and this thread immediately caught my attention because I had the same problems that I fortunately overcame (I'm now able to talk with any woman I want with absolutely no problem). I'll try to reply to the first post and other posts of Bronson99. If you have any other questions, feel free to ask and I'll try to help.
Will doing this confer any benefit whatsoever?
Merely saying "hi" to girls is only the first step that I would recommend only to people who have no social confidence whatsoever. Since I guess you aren't so shy that you're afraid of saying hi back you should try something more difficult, that is start an actual conversation.
So the other question is, should I say anything besides "hi"? If so, what?
Yes, you should start talking with them!
You say you have a place where you go to exercise and some girls there say "hi" to you. Man, most shy guys only dream of such opportunities! If a girl says "hi" to you, it's super easy to start a conversation.
I personally like to start a conversation with the first simple thing/observation that comes up to my mind, e.g. "hey there, I saw you from over there and just couldn't pass the opportunity to talk with you. What are you up to?". If you're confident enough to start a conversation in a more direct way you can say something like "hey, I find you very sexy and I just have to get to know you. I'm XYZ".
I bet you're now thinking "okay, and what should I say later?". The second part (actual conversation after the opener) depends on the venue, response of the girl (some girls just don't want to talk, and that's okay - it's not your fault), things that she says, etc. Just to give you a simple idea here's an example of a conversation:
Girl: Hi!
Guy: Hi there! I saw you when I was walking on the treadmill and just had to get off it and find out more about you. I'm XYZ.
Girl: I'm ABC.
Guy: Nice to meet you, ABC. What are you up to, bench pressing 500 pounds?
Girl: Haha, no, I'm actually waiting for my personal yoga trainer.
Guy: That's cool! To be honest with you, I hate walking on the treadmill. Will yoga help me become as ripped as Jason Statham?
Girl: Haha, I doubt it, but you can try!
Guy: Definitely! What about you, why yoga?
and so on. Your goal now should be only to start a conversation and exchange at least a few sentences. If you're confident enough, ask for her number at the end. Don't make it a big deal - say something like "it was a pleasure talking with you, I would love to get to know you better. What's your phone number?". DON'T say "can I get your phone number?" or anything like that because it just sounds needy. Be a man and tell her to give you her number. If she refuses that's okay (don't take it personal), you can either keep talking and try again later or say bye and be on your way.
Try to instill in your mind that all these girls who say hi to you are BEGGING for your attention. They are so desperate to talk to you that they say hi first! I don't care if it sounds ridiculous or arrogant for you at this point. It's a mindset that you should develop in order to be able to talk with every girl.
The ultimate goal I suppose is to help me break down the barriers I have.
That's a good plan, taking it step by step is IMO the best way to go. However, you have to keep in mind that you should constantly do more challenging things.
I mean, I can't speak to the opposite sex, because I believe I come off as strange, vapid, and idiotic. Then if I can break down that barrier, then maybe I could meet a girl.
That's only your belief. Of course if you believe in it, you'll probably project it while talking with other people. That's why your job should be to talk to as many women as possible and focus on the conversation, not your beliefs. Keep in mind that the longer you hesitate after you see a girl you would like to get to know, the more excuses you'll come up with.
I don't mean dating, though. (So call me shallow, I just want to "hook up" and that's it. I just want to get it over with, man!)
I understand that some guys only want to have sex (especially virgins) but if you approach a girl with a desperate "I want to get it over with" belief, you'll come off as a desperate guy. Focus on talking with girls first. You can learn how to create sexual attraction later when you deal with your self-limiting beliefs.
With everything like this, I *always* look for the risk. My mind finds many, but the most obvious is gaining a reputation for being "that strange guy who talks to girls who don't like him."
Unless you live in a small town and do something really stupid you won't gain this kind of a reputation. You're a human being, and human beings are social creatures. If a girl doesn't want to talk to you, it's her problem, not yours. There are many other girls who will talk with you.
Eh, it's not like I would just meet this random girl at the park and the 2nd time I see her, I'd suggest that. I know it doesn't work like that.
But I'm hoping I might be able to "luck" into a situation. If I don't try, then I have zero chance, y'know?
It can work like that if you're very confident, but I wouldn't think about it now. As for luck, the harder you work, the luckier you are. You will create numerous opportunities when you simply start talking with girls who say hi to you. However, don't obsess over sex. Don't try to look for a meaningless one night stand just to get over with it. If you don't transform yourself, it won't make much of a difference.
But I thought it's a general rule, you cannot just ask for a girl's number after meeting her once.
And... what would make you think a girl would actually give me her number anyway? What girl--you tell me--would give their number to someone shy and awkward with low confidence?
Whose "rule" is it? How are you supposed to get a number if there's a "rule" stating that you have to meet her twice? What if you live in a big city? Your chances of meeting her again are slim to none. What if it was your perfect dream girl?
What would make a girl give you her number? The answer is simple: making her feel better in some way. If you forget about your beliefs that you're shy and awkward and focus on making her smile, I'll guarantee you that pretty soon one of the girls you'll talk to will give you her number.
Okay, this post is already too long. I hope it's helpful. If you have any other questions, feel free to ask.