In every design, there is a process. Many experts describe it in a very linear approach, but the reality is different. It is very dynamic and iterative, with many fails and learning.
The primary skill that UX designer must have is empathy, listening and examining of users behavior. I would say understanding human psychology is crucial as well.
With that in mind, you will want to do a lot of research based on interviews and usability test techniques. You want to empathize with the user by asking questions and observing while they use the product.
The second most important skill is to read and understand the data. Collecting and analyzing data should be part of the rituals of every UX process. Data can tell you how many users are doing something, and you can make good decisions relying on it.
Workshops and Collaboration
It's good for every designer to organize collaborative workshop sessions with internal stakeholders and external users. Those workshops are vital to creating empathy maps, user persona, user journey mapping, and strategy. But also, they are precious to innovate through collaborative play.
Information Architecture (IA)
Information architecture is about helping people understand their surroundings and find what they're looking for, where they expected it to be. It's on the websites we use, the apps and software we download, and even the physical places we spend time in. Good organized and intuitive navigation is an example of excellent IA work.
Information architecture is a backbone of the design structure that you can translate into wireframes of the project.
IA is the foundation of UX and one of the many requirements that designers must respect.
Sketching wireframing and prototyping skills are essentials to quickly visualize and test all assumptions that the team can have and finally validate through the usability tests and research described above.
You don't need UI and Visual design skills to be a successful UX designer. Visuals are at the very end of the process after many iterations and tests before handing them over to the developers. In many bigger organizations, it's a different person who will care about visuals and UI delivery.
Once the product is live and ready to use, you want to test, measure and repeat. Don't be afraid to fail, but learn fast and do it again.