The career opportunities in Web design are plentiful, and if you have a background in graphic design, transitioning into the field isn't out of the question. Truth is, the two jobs have a good deal in common. Web designers need to have an eye for layout, just as graphic designers do. They both need to have good people skills and must be able to take ideas and translate them into a visible "product".
Having a background in graphic design is actually a great first step toward becoming a Web designer. The next step would be to get some specialized training in areas that are needed to do work on-line. Taking a class or two in things such as HTML, Photoshop and other related subjects can help prepare you for layout work on the Web.
One easy way to move into the field of Web design is to see if there are any positions opening up in the company you are working for right now. You'll have the advantage of an established track record as a good employee, plus you will already be familiar with the company ideas and ideals. This can put you one step ahead of other applicants and give you an edge on the competition. They may even be willing to provide you with training.