A few years ago I committed to improving my social skills as much as I could. I had a stretch of about 6 weeks where I went from being anxious to give my order to the waiter to making a new friend at a bus stop. Here's what I did:
The first thing is that I understood I had to stop watching content and actually go outside. You can't learn socializing by reading books, in the same way you can't learn to play football by reading books.
So I committed to going outside and being where people were at least 3-4x a week. This meant that I went to the library to study, I joined the gym to work out, I'd eat lunch at the public cafeteria, I'd say yes to anything that got me out of the house. Anything.
From there, I had as many low stake interactions as possible: I asked the cashier how their day is going, I'd ask the waiter what they recommend on their menu, I'd ask for time or directions to people on the streets. This gave my brain proof that engaging with people is safe and even quite enjoyable.
Once I got more comfortable, I progressed by talking to the people around me, while still keeping it short and low pressure: I'd talk to the people I saw at the gym, I'd ask homework questions to my classmates. I made it a mission to have 1 interaction with a stranger daily.
Eventually, I tried more intense places like parties, bars, pubs, clubs, sports events etc… And I engaged with people there in the same way.
The habit that made a difference for me was that I'd write down how each interaction went: what happened, what I did well, what I could have done better etc… So for every interaction, I knew what to pay attention to.
The most important part of this is the momentum. After I did this for a bit, it felt incredibly easy. I kept gaining positive experiences when talking to people. I've gotten rejected as well, but the goal was to talk to people, not to get the contact. By the end of it, I gained a much better intuition of how to initiate conversations, what to say and what to not say.
One insight that helped me a lot when doing this: you don't have to be in a good mood to talk to someone. You can actually be in a shitty mood, embrace it and still talk to people. Once you do, your mood tends to naturally improve on its own.
Beyond this, I studied how to express and communicate with people in an authentic and charismatic way, I'll make another post about that in the future.