Why You Need To Directly Practice Your Social Skills
To improve your social skills you have to practice them.
That sentence is one of the most important ones on this site. All the advice here can help you have a better idea of what or not to do in social situations, 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 find the same advice in dozens of other places. I still have to mention it though because it's so crucial.
If your interpersonal skills are unpolished 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 and put in the hours to catch up. You need time to become familiar with all the little details everyone else learned years ago.
You have to put yourself in a variety of circumstances, try out different methods of interacting with people, make your inevitable mistakes, and slowly get the hang of things. With practice, situations you used to awkwardly bumble your way through will turn into ones you've come across plenty of times and know how to handle. Skills and traits that are forced and stilted at first will become second nature, and almost feel like you've always had them. You'll be able to think quickly on your feet. You'll start to gain a confidence that comes from realizing you've been around people successfully before, and you can do it again.
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. It's usually easier said than done to just read about a way you should think and instantly change how you look at the world.
Learning by observation is also useful
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 what you notice into your own personality and style. This goes for learning positive new concepts to use, but also things to avoid. It's good to be open to learning from anyone. You may not be super-keen about someone 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. It can also happen unconsciously. As you hang around people enough, certain traits of theirs will rub off on you without you noticing.
Practicing specifically what you want to work on vs. spillover effects
A point on what types of practice experiences to seek out: 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, say, mingle at raucous parties. One is rehearsed and pre-planned, the other is more improvised and spontaneous.
There are lots of different ways to socialize. Catching up with 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 won't make you a ton better at cracking jokes and being the life of a party. If you want to improve at a specific skill, like being able to think of things to say in group discussions, then put yourself in more settings where you can do that.
At the same time, getting better at one type of socializing can have spillover effects into other areas. Like 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 might 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.
While practice is important, diving into social situations totally unprepared can be counterproductive
When I say "practice" I'm not suggesting you blindly force yourself into scary interactions you don't know how to handle and hope for the best. That's just setting yourself for failure, discouragement, damaged self-confidence, and reinforced anxiety. You need to prepare by reading up on how to handle the situations you have trouble with (e.g., how to start conversations and then keep them going). That way you'll have a rough starter plan going in. If a type of conversation makes you quite nervous, you'll have to find an approach that helps manage your fears.
Where to practice
This article covers some places where you can rack up that practice time you need: