How?
It simply takes practice.
Popular kids have been 'honing' their social skills literally since they were 4 years old. They have been paying attention to other people.
Notice how the sociable kids might have done more poorly in class, whereas the introverts maybe did better? The sociable kids are attuned to relationships. While your thoughts were on the math problem, theirs were on 'how xyz is not paying attention to me, and why'.
There are people you can hang out with. If you try to stay 'in the present' and actually practice paying attention to their thoughts and emotional signals, they will like you.
Unless you literally have autism, there's a 100% chance that you can be sociable. Also - take heart with the fact that most people find it difficult to interact with others. Want to know a secret: many extroverts, who are socially attuned, are actually quite nervous among others, always watching what they say, being deliberate with their actions. So don't feel alone. You're in the majority.
If you fail completely, you might be trying things too far out of your confidence zone. A mousy introvert isn't going to morph into a charismatic rockstar within a single leap, no matter how much the introvert might want that to be the case. Odds are, he'll seize up and freeze, in which case the only thing he practices is the act of freezing.
Another friend was terrified of public speaking so started doing stand up comedy, and now helps run one of the regular shows in a pub here.
You have to put in the hours to an extent, it's not just a case of trying a couple of times and giving up. Alcohol helps to a degree, but obviously don't go crazy with it. Probably hanging out with extroverts and taking note of what they do helps as well.
I'm past 30, grew up as a archetype semi-aspie geek kid with little interest in social matters, preferring books to social settings. My preference is to my own company, still, but I'm comfortable in social settings, I'm a fluent communicator and commended for my presentations when I give them out. I'm also blessed or cursed with a complexity that makes me look perpetually 15 years old - and I'm short. Yeah, goodbye professional credibility based on halo-of-appearance. The upside is I can introduce my two kids early in any conversation, thus signaling my actual age and status - which usually results in a sudden episode of massive cognitive dissonance to my amusement.
So, there are handicaps, and, there are social skills. The dynamics underlying social skills can actually be learned from books - but, like any craft, actually acquiring a functioning ability takes practice. For me, I would split matters under "social capability" to three categories: 1. Self-confidence and Dealing with anxiety 2. Individual interactions 3. Group dynamics.
1. Dealing with anxiety and acquiring self-confidence. For me this is first and foremost a physical activity consisting of a) good posture b) calm and friendly air and c) deep breathing for calming the nerves. A corollary to this is the functioning of mirroring in any social setting - you start to behave, as others percieve you to be [https://en.wikipedia.org/wiki/Mirroring_(psychology)]. So, if you appear first as mousy, people treat you as mousy, making you feel more moysy. If you appear as confident and amicable, people treat you as confident and amicable, and you start to feel more confident and amicable.
I actually had to take a few months of personal trainer lessons to fix my posture and gain some physical fitness (I requested a program consisting of mostly of body weight exercises and I can't recommend them enough).
If you don't have a good physical posture, and don't have at least a minimal exercise routine, these will actually help a ton. I can give some references on materials if anyone likes.
On anxiety and introspection - zen meditation helps. "Sit down and shut up" by Brad Warner was a good, no-nonsense, introduction. No mystical crap.
2. For me the best resources have been interaction with colleagues and friends, Dale Carnegie's "How to win friends and influence people" and the courses http://www.thegreatcourses.com/courses/how-conversation-work... and http://www.thegreatcourses.com/courses/negotiating-the-best-.... The last is about self-confidence -as some interactions are confidence plays, it really, really helps a ton to be aware of the rules.
The hardest part for me, still bugging me, but the most important one as well: remembering people's names! This is absolutely the fundamental cornerstone of every interaction.
3. Group dynamics is a bit different. The simplest rule is: do what everyone else is doing. Go sit at the same table. If there is someone you don't know, introduce yourself. Here also comes the "how conversation works" great course into play. There are different kinds of conversations - learn what they are.
One of the secrets of human relationships that I only got recently that the relationships are things that are in peoples head's. There is no "single relationship" - each relationship is composed of the presentation of the interaction in the head of each participant. This means, that although you may feel awkward, the other person might feel the interaction is natural and pleasing. This is where mirroring, and keeping confident pose comes into play. If the interaction goes on for a long time, you start to mirror the other persons view of the relationships. But, there are still two copies of the relationship - in both of your heads.
So, I would suggest, step 1: air of confidence - good posture and smile. Wait for serendiptous things to happen. Make sure you are dressed neatly and so on - this is part of the mirroring dynamic.
Someone might feel "But that's not authentic me" - sorry - you can't change the humankind or basic psychology of those around you, you can only adjust and learn.