Why You Need To Directly Practice Your Social Skills
To improve your social skills you have to practice them. That sentence is probably one of the most important ones on this site. All the advice on this site can help you have a better idea of what to do or not to do, but you still have to hone the actual skills in real life. It's the same for any other ability people can have. This point is really basic, and you can read the same advice in dozens of other places. I still have to mention it though because it's so important.
If your interpersonal skills are a little shabby, you've likely spent much less time socializing compared to most people. Some combination of your personality and your life experiences has caused you to miss out and fall behind your peers. You need to get out there as much as you can and put in the hours to catch up. You need time to become familiar with all the little things everyone else learned years ago.
You have to try out all the different aspects of interacting with people, make your inevitable mistakes, and slowly get the hang of things. With practice, situations that you used to awkwardly bumble your way through will turn into ones you've come across dozens of times, and which you know how to handle. Skills and traits that feel forced and stilted at first will become second nature, and almost feel like you've always had them. You'll start to gain a confidence that comes from realizing you've been around people successfully before, and you can do it again.
Learning by observation is also important
You have to directly practice skills like making conversation. While you're around people, you also can't help but take in what everyone is else doing and incorporate some of the ideas you pick up into yourself. This goes for learning positive new things to do, but also what to avoid. It's good to be open to learning from anyone. Sometimes you may not be crazy about a person on the whole, but you could still pick up some good isolated skills from them.
Like with direct practice, this process is gradual. You won't change overnight just from watching people, but eventually the benefits will pile up. It's another reason to simply spend more time in social situations. At times the observation process is conscious and deliberate, like you'll notice someone has an effective way of introducing themselves, and decide to do the same thing. Just as often, it all happens automatically. As you hang around people enough, certain traits of theirs will rub off on you without you noticing it's happening.
Attitudes have to be practiced as well
Your social success will partially be determined by your attitudes; how confident you are, how positive your self-image is, how optimistic you are, how you view other people, and so on. Helpful attitudes have to be built up over time too. They're quite abstract and psychological, but they still have to be earned through real-world experiences and successes that support feeling that way.
Practicing specifically what you want to work on vs. spillover effects
A point on what types of practice experiences to seek out: There are lots of different ways to socialize with other people. Chatting to someone over coffee isn't the same as debating them. In one sense, you'll get good specifically at what you practice. Learning to have deep conversations with people won't make you all that much better at cracking jokes and being the life of a party. If you want to get better at something in particular, like being able to think of things to say in group conversations, then put yourself in more situations where you can do that.
Sometimes someone will take up an activity like public speaking, hoping it will help them get along with people more easily, and then later find that the skills needed to give good speeches don't 100% translate into helping them chat to people at social gatherings. One is rehearsed and pre-planned, the other is more improvised and spontaneous.
So on one hand, try to directly work on the things you want to get better at. But it's obviously not that cut and dry. Getting better at one type of socializing can have spillover effects into other areas. To get back to the example from a second ago, becoming a good speaker may make you more confident and polished on the whole. Your sense of humor, or ability to tell a good story may improve. Learning to handle the nerves from speaking before a crowd may make you more at ease in smaller groups. Realistically you'll end up doing a mix of specific and indirect practice. It all helps in the long run.
This article covers some places where you can rack up that practice time you need: