You just gotta put yourself out there. That's how it works.
You'll read that and snort, "Oh that's easier said than done." and you'd be right, but you just have to force yourself to do it. Talk to the person who sits next to you in a class; ask to borrow a pencil or something. Ask them how they did on the last test, or if they got question 10a wrong too and "oh that Mr. Jackson is a real hard-ass." Even if you didn't. Follow their cues. You have to fake it until you make it sometimes.
You really just have to not overthink things and swallow your awkwardness and put yourself out there. I think you'll find that it's a lot easier than you've been making it seem in your head.
Trust me, I was homeschooled from the time I was about four or five until I was about seventeen and my parents forced me into junior college.
Up until that point my only real long-term "friends" had been my little brother and my dog (there were some other non-relative kids here and there along the way, but I never stayed in touch with them for long). The only other people I knew were on the internet, and that went also for girls (protip: never fall in love with internet ladies as a minor with no means to close the gap because you will go insane). It was a pretty dark and shitty time in my life, being seventeen, not wanting to be in school because you were depressed and would rather sleep all day, had no concept of how to do schoolwork or will to do it, and were an incredibly lonely virgin who thought they'd always be that way.
It took some time to come out of that shell. People eventually started to talk to me in classes and I would talk back; the professor would say or do something funny, I'd look over and laugh with the person next to me, eventually that became discussing schoolwork; eventually that became talking, eventually that became hanging out on break or after class, eventually that became hanging out off-campus, and eventually you meet new people from that person in much the same way, and you start building your network.
I don't even talk to the guy who started talking to me in that writing class anymore, but through him, I met someone else, through her I got absorbed into this huge group filled with drama and idiots and assholes, but when that group shattered, I came away with a few exemplary people who I call my best friends to this day; I even wound up with a couple steady girlfriends and all kinds of crazy sex from the whole thing.
And now here I am writing this from a real university where I'm taking classes in subjects that I want to make a career from; I have friends and a life and everything is pretty A-okay.
But it wasn't easy. Meeting people is hard (and I admit it's still hard). Meeting women is doubly hard (ditto). Succeeding is hard. Life is hard. But you just have to just have to put your head down and push and never stop pushing. To stagnate is to die; you gotta keep moving like a shark. You have to stop psyching yourself out by overthinking every little detail of everything and the myriad ways you could fail (this was, and is, my case; I'm not sure if it's yours, but you have to identify what's holding you back and then do the opposite of that it says).
And you will fail; you won't make a connection with someone, or you'll find out they like dubstep or are into illicit activities or something and you don't want any part of it; that's fine, as long as you keep moving, and as long as you don't use every excuse you can to not keep pushing (overlook some flaws).
I'm writing a novel here, but there are few things I enjoy more than trying to help people find and pursue their potential.
Just put yourself out there: talk to someone in your class; set up a study group or start small and try to find a study buddy even if you don't need one; if you can't find one in one class, try the next; if that doesn't work, meet someone at the gym, ask about a workout routine or how to do a certain exercise; overlook minor flaws and meet new people through them; don't make excuses not to try, don't overanalyze, just do. I've been where you are. I know that feel bro. But I also know that if you put your nose to the grindstone, you can overcome it because you've already gotten in shape and learned to dress, and this requires the same discipline, just in a different way.
No excuses.