The 101 of friendships and relationships in life is a certain ability to (a) Take some risks (b) Take the initiative Instead of waiting to be invited to something try to invite others. There might be occasions you will be left embarrassed or feel rejected but if you don't try, how will you succeed? Think of it like childhood: If you're not willing to fall how will you learn to walk? If you're not willing to speak gar…
Eliminate habits that repel others and work on habits that attract them.
Don't be annoying. Don't try to make things about yourself. Don't correct people. Don't offer unsolicited advice. Don't be creepy to girls. Don't be pushy. There are myriad ways to be annoying.
Be pleasant. People strongly remember how you make them feel, so be sure your influence is positive. It's better to leave them wanting more than overdoing it and making them sick of you.
You can't be the judge of whether you are socially attractive or repulsive. Only others can do that. Don't fall back on ego-preserving self-deception, but accept their judgment and learn from it. At worst, the group isn't a good fit for you, in which case it's best to gracefully move on. The particulars of an intramural football team are going to be very different from the those of a math study group. Look to join groups that play to your strengths and not to your weaknesses.