I certainly would not call myself an example of highly developed social capital, but I do think I've managed to bring my general socio-emotional skills up from "abysmal" to "ok" over time, in that I actually *have* more than one total friend now and also can perform well enough socially to impress at a job interview.
I started with reading blogs/books and also watching social skills youtube videos, but ultimately in all those cases, things worked best when I combined them with practice. So each time, I would identify a social skills task I was struggling with, look up tips about that, *and then practise them the next time I talked to someone*. Generally when I did this I felt an immediate improvement in the length and quality of conversations I had.
One thing that was very important for me to learn is that if you don't bother to seek people out, they often won't bother to seek you out. So you can't wait around until the other person remembers you exist - if you want to get closer to them, you need to go ahead and get in touch with them. And the more time you spend with them overall, whether that's in person or talking over some sort of messaging, the closer you'll become. So if you are thinking, "I have no friends and I'll never have any friends!" but also you haven't talked to someone on purpose for months, well, that is probably why. And if you do tend to be bad at remembering to message people (I'm very guilty of this), don't start every message by apologising for not talking more often, just go on to whatever you actually wanted to talk about. If you apologise each time for not talking I found you just get in a cycle where the whole conversation is spent apologising which isn't a great vibe honestly and caused me some communication issues when I did it.
If it's not socially acceptable in your area to talk to strangers on the street, or if you just don't have the confidence to do that, the main other ways of meeting people are by going to some sort of meetup / group / hobby class, or by getting people you already know to introduce you. If you meet someone intriguing at a meetup or group then you will need to follow up at some point by asking them for contact details and then remembering to contact them or you'll end up having them as an acquaintance that you only ever talk to at the group. With the introduction method, this can be a great method if one of your friends or family members is a lot more socially skilled than you, because you can get them to do the scary part of initiating the conversation in the first place, and you get an initial boost in the conversation by being introduced by someone who is already making a good impression. But again, if you want the new person to be *your* friend and not just your mum's friend or your friend's friend you will need to talk to them of your own accord afterwards. Basically, all social relationships need to be maintained by occasionally dropping someone a message at minimum, or people will assume you're not interested.
Also, as has been mentioned, while it is possible to have a lot of social connections while being emotionally not skilled, a sound base in emotional skills will improve the quality of all your relationships.
This includes things like knowing when and to whom it's appropriate to vent. Complaining and venting is a healthy part of dealing with negative emotions, but I've found that if you vent to the wrong places or people, it can cause issues, so it's best to match up your venting to people who you know will be down to sympathise with you on that particular thing. And in general, more broadly, it's ok to have different friends or groups of friends for different things. For instance, if I wanted to talk about money, I would talk about it here, not to my friends who are WL0 or WL1. If I want to vent about being upset by a family member, I will take it to a close friend I know will sympathise, or to a discord server I'm in where that sort of content is welcomed. If I want to ramble about the latest fictional series I'm obsessed by I will talk to friends who I know are into that sort of thing. If I want to vent about certain political issues that I don't hold a mainstream view on I message my friend who is open to non-mainstream political theories. Basically, successfully matching the conversation content to the person tends to strengthen all of the relationships and avoid straining them.
Other emotional skills include healthy setting of boundaries and dealing with conflicts. Getting these in place means the friendships are far less likely to blow up in your face further down the line.
The other thing I tend to do these days which is a change from when I was younger is that I try to assume that everyone has something potentially worth befriending them over. I used to have a bit of a superiority complex about being smart, or about people who watch soaps and suchlike, but these days, I try not to judge people before I know them, but just be open to whatever connection can come about. People who don't have the same strong points as you often have different strong points that can really benefit you, and you never know what you'll learn from someone or what sort of unexpected things you might find out. And you can find that you get to at least friendly acquaintance level with people you thought were quite different from you.
Ultimately the point of befriending people isn't just transactional and getting them to do stuff for you. The connections have value all by themselves, you've got to see your friends as *friends* and not some sort of social vending machine. And if something does come up that you know how to deal with easily and they don't, then it's your turn to put something into the relationship. This isn't always something that you see as a chore - for instance, I often take my ukulele to social gatherings. I like playing ukulele! But it still counts as me putting something into the friendship because my friends don't know how to play the ukulele and quite like having the option for some live music.
I think somehow in a larger social group, the group can also accomplish things a lot more easily than if everyone is just doing their own thing.