From someone that went from being a complete loser to a social superstar, I'll give you a few tips. To be honest, the serious posters on this thread have all said some pretty legit ****.
Stuff like first making friends, having mutual hobbies, and being confident are all true. However, I've been in a similar position from being widely hated and picked on, and then I grew into a person who was very popular in social aspects and with girls/women. Perhaps I can give you some insight from my experiences to help you understand better.
It's difficult to become a "new" person in an "old" environment. You hardly go anywhere, you say the only place you can meet girls is the mall. To me, this implies that you have limited means of transportation and/or limited income.
You wanna be socially acceptable at 18 years old, you should get a job, a license, and a car. 100% incontestable fact is that you are automatically a more likable person if you are self-sufficient, and even more so if you can provide for others. Suppose you manage to get lucky, you chat up a shy girl who shows enough interest in you that she would like to get to know you better. Well too bad if you can't take her out to eat because you've got no car and no money. Make sure you cover your bases. You need roots from which to grow.
When I was in 7th grade, I had already suffered through years of consistent bullying every day I went to school. I hated school, and stopped caring, and as a result, I got left back and had to repeat the 7th grade. That meant that all those bullies that I had to suffer all were now 8th graders, and I got to meet a whole new group of people, the new 7th graders. When I realized this, I made the decision that I did not want to be a loser any longer. To be honest, I did exactly what Jam first suggested to you. I saw a pretty girl on the first day of school at recess, I walked up to her, and I complimented her, and she smiled, and I walked away. That girl eventually became my best friend for the next 2 years, and she was one of the hottest girls in the class. Additionally, I made friends with SEVERAL GUYS. This increased my social status because when you're a guy, and you're walking around confidently with other guys, people automatically assume you are a cool guy, unless you do something to make them think otherwise. Just looking presentable with other presentable looking people is enough. I wasn't a social superstar at this point, but I was enough of an average joe that I didn't have to go to school worried about getting bullied all the time.
Of course, my social skills didn't grow in overnight. But let's face it, when you're hanging out with a bunch of fresh dudes, and you're consistently seen with one of the hottest girls in the class, which ALSO means that you're hanging out with her and her friends, who are also hot, these things automatically shoot you up the social ladder. From there, I was just myself, and I learned to weed out those "annoying parts of me" (because let's be honest with ourselves here, there's a difference between being yourself, and being annoying).
My experience is not going to be the same as yours. You have no social experience. I had negative social experiences. I was 13/14 at my turning point. You are 18/19. In some ways, you will have the advantage, and in some ways not. But when I decided to "go walk up and say hi" I think the number one thing that encouraged me and also that made me successful was the will to change my social status. I distinctly remember the following internal dialogue.
"Wow, she's really pretty. Too bad she would never talk to a guy like me. I wish I was one of those cool kids that could get a girl like that. Well wait a minute though, nobody here knows me. No one here knows I'm a loser. In fact, I could just try to be cool, and I bet no one would ever know the difference. Maybe I'm not the most handsome, buff guy in the world, but I'm not ugly. You know what? **** it. I'm gonna walk up to her all cool and tell her that she's beautiful. Well, maybe I won't say "you're beautiful." That's probably coming on pretty strong, and it'll probably seem pretty creepy. I gotta look like a naturally cool person who is out scouting, trying to find other cool people to associate with."
And then I walked up to her with my 7th grade wannabe cool strut, and I said, "Hey, you look pretty popular." And I smiled, and Brittany smiled back, and I walked away.
There is nothing that I learned that made me cool. Nothing about me changed. I didn't have swag, nice clothes, or experiences that gave me an advantage. I just had the will power to be the person I wanted to be, and I grew into that person overtime. Taking the first step was a little nerve wracking, so I made it a short experience. But as you can probably tell, that was a defining moment in my life.
When at a neutral point, people respond to politeness with politeness, and to cruelty with cruelty. If a person isn't like that, you probably don't want to associate with them in the first place. When approaching a person, don't be awkward, just be confident. If you aren't confident, fake it. CONSISTENTLY fake it in all aspects of your life. This will turn into actual confidence because as you practice it, it will become you. I do not approach problems thinking "I cannot solve this". If you really believe that, then why even bother trying. Believe in yourself, and your abilities to overcome, because they exist, even if they are currently underdeveloped.
To close, I'll give you a hypothetical analogy. Suppose you had never lifted anything in your life, and you were very weak. The best way to approach this is probably to begin lifting light things, and believing that eventually, if you exercise enough, you will become stronger. Overtime, you become more and more powerful, and you find that the problem of being able to lift heavy things disappears, because your muscles have developed.
Everything in life is like this, including being social and talking to girls. As long as you approach it with the correct mentality of "I can improve in this aspect" then you will. This I promise you.