Well shit. 1. Get her number idc if your non-social, you can fucking do it. She will most likely give it to you. Ask for it, if she gives it to you your already in it, if not she wasn't for you anyway 2. Use that damn number you got and text her, say something to start like "I'm that dude that came from nowhere that got your number, how's it going." don't text her every damn minute of your life, don't "sweat her" 3. After a week or 2 of texting and talking ask her out on a date to somewhere like bowling, food, go-karts, walk, anything. If she likes you back she will most likely accept anything. 4. If she doesn't cancel the date like this last girl did to me at the last minute then your good to go. Be yourself try to learn more about her than you telling her all about yourself. 5. After the date if mood is good and right you might get a kiss or something at the end, if not don't sweat it. 6. Text her back after the date that you had a good time, and you should be good from there. This is the 2015+ way to get a girl as of now. 7. Don't forget to continue the dates.
From reading your post, I can tell you are an introvert and it's nothing wrong that. I am too an introvert. However, it is in your power to change that.
As far as getting a girlfriend, the only solution I can think of is talk to more girls. Talking to girls isn't as hard as it seems. Just remain calm and talk like you are having a normal conversation with someone. Don't talk about sex, politics, your opinions, or other topics that makes you look egotistical.
Sit down and think about the things that interest you. Join a club or take some classes regarding whatever it is that interests you the most. Don't worry too much about dating. Just try to meet people in general and spread out. You'll meet people, including women, with time.