It's a fair question. I don't think there is one simple answer, because a lot of it will depend on the child.
I think a lot of it is about exposure - basically ensuring that your child has lots of opportunities to interact with peers in lots of different settings.
But I think it's also about observing your child's interactions with others and giving them timely, constructive feedback about how they might be coming across, how other people might be feeling in response to their words and actions etc.
Sometimes it is about getting your child to reflect on their own interactions for themselves, ie encouraging self awareness and getting them to consider how others might perceive their words and actions. This is key in my opinion, as a lack of self awareness is often the biggest problem.
Sometimes it is about rehearsing difficult situations or conversations with them in advance so that they can think through how they want to handle things. Sometimes it is about problem solving and brainstorming practical strategies to deal with challenging social situations.
I think it's really important for children to understand feelings and emotions - starting with their own but then extending to those of other people. They need to develop their capacity for empathy. So, lots of talking about their own feelings and making sure that they have the language to recognise and identify feelings. Talking in an age appropriate way about your own feelings. And talking about how you think others might feel in different situations - that could be characters in books and TV programmes as well as real people. Really unpicking what might be going on for those characters in any given moment, understanding the feelings and motivations that might underlie their actions etc.
I do accept that all of the above is probably much more difficult for parents who haven't ever had the opportunity to develop good social skills themselves. It won't come naturally to them, but I think they owe it to their kids to try. I think there are various books etc that might help as well. And many parents may also have relatives or friends that could be enlisted to help with some of these things.
I actually think that a lot of it is simply about where you choose to put your emphasis. My dd excelled academically and in various extracurricular activities and she knows that I am proud of all of her successes. However, she also knows without a shadow of a doubt that I am far more proud of the way that she treats other people. Being kind, treating others with dignity and respect, recognising that everyone has different strengths and talents, understanding that everyone has equal value... these were things that dd knew were way more important to me than trophies and test results. And those things became more important to her as well.