A Web designer is the person responsible for determining the look of a website. They design the layout, the colours, the fonts, and all the visual aspects of the site.
The following questions detail some of the common aspects of working as a Web designer for a company (not freelancing). The more of the questions that you can honestly answer "yes" to the more suited Web design is to you as a profession. Remember, however, that Web design is only one way to work on Web pages. There are also jobs as Web programmers, Web producers, web writers and graphic artists, and Web freelancers. You may be better suited to one of these professions.
Most Web designers love the Web. They browse it a lot and love looking at other Web pages. While it's possible to do the work without enjoying the medium, if you don't like Web pages, eventually designing them will start to annoy you. If you aren't interested in the Web, then looking for a job as a Web designer isn't a good idea.
While not all designers feel they are artistic, at its heart, Web design is an art form. Most designers have a goal of making pages that look good and meet the customer and client needs. While you don't need to be able to draw or paint to be a Web designer, you do need to develop an aesthetic sense so that you can see when things are working and when they aren't.
Many Web designers come from a graphic arts background. This is a great basis for a career as a Web designer, as long as you remember that Web design is not the same as print design.
Web designers focus on the visual design of pages.
Web designs start with layout. If you would rather work with graphics you should think about Web graphic design instead. If you'd rather work with text, you should consider Web writing.
Web design is ultimately a computer art form, and if you don't feel comfortable on a computer you won't feel comfortable in this career. But the benefit of being a Web designer, rather than a Web programmer or Web producer, is that you don't have to learn HTML or learn CSS if you really don't want to. Many Web designers work solely in WYSIWYG editors and leave the coding up to the programmers and producers on their team. It is even possible to get a job as a designer working solely in Photoshop, but that is less common.
I recommend that you spend some time learning the basics of HTML and CSS so that you know what the languages are capable of. And most hiring managers will expect you to have some understanding of the languages. But unless you're on a team without a programmer or producer, you don't need to spend a lot of time on the languages. You should know more about principle of web design.