Web page designer skills for your resume and career

Three soft skills stand out most: an ability to see the big picture, an ability to "read" people, and an ability to make a convincing argument for your design solution(s).
i. An ability to see big picture: there are an infinite number of details in graphic design, whether you work in website design on the front or back end, or in print media with physical outputs. It's easy to get caught up on the details, especially when clients are making specific demands about things such as paper type. A skilled designer must be able to see beyond the details and look at the big picture for an effective design solution. For example, a client may be asking for an invitation design for an up-coming event. A skilled designer will ask questions and dig in, eventually uncovering that perhaps for a successful event, the client also needs a splash page and social media, either in place of or in addition to an invitation. A skilled designer addresses design problems holistically, rather than minutely.
ii. An ability to "read" people: designers are trained in art-specific vocabulary. Hue, saturation, pixels, gestalt...most non-art folks don't use or speak that language. When clients are describing their goals, they aren't using art-vocabulary. It's a designer's job to translate what the client is saying into an advanced and effective creative solution. They must be able to speak and understand the language of non-creative folks, as well as the language of the broader creative industry.
iii. An ability to make a convincing argument for your design solution(s): many young and inexperienced designer tend to get their hearts broken when a client smashes one of their [very well thought-out] ideas. Rather than rolling over, a designer must learn to navigate how best to build support for their idea(s). That might mean in some instances you work more fluidly with the client throughout the design process, so that they feel they have ownership in the development of the solution. In other instances it might mean that the designer is presenting options, rather than a single solution, so that the client feels empowered to make choices throughout the design process. And in some instances, it might be a matter of better explaining and presenting your idea to a client; perhaps the designer needs to push back more, perhaps they need to provide more research as to why their solution is best, or maybe they simply need to present it with more excitement and enthusiasm.

I don't think the skill set needed will change much from what it has been. Qualities that come to mind are: teachable, reliable, thoughtful, articulate, adaptable, engaged, critical thinker, technologically adept, able to think big and small, empathetic, and good listener.