G. Mark’s Answer
I have found that engineers tend to be trained in more than one area, but there is significant overlap between many areas of engineering. The general global engineering process -- the approach to solving any problem from definition to development and maintenance -- is the same. That being said, you would approach a career in structural engineering like any other engineering specialty. You would first choose a school in engineering to get a degree. The nice thing is that you'll have many of the same undergrad requirements for all engineering until you branch off and specialize. This will give you not only a good idea of which are you'd be best suited for -- and by extension, whether you're suited for structural engineering -- but will give you a good and sound base of education to pursue your goal.
If you decide that this area of engineering is a good fit for you, you can apply for co-op positions and then internships at companies that look promising.
Once you get your degree, and you'll be best positioned for employment at a firm you've interned or co-opped at, you can look for job listings that mention your chosen area. The takeaway from this is to start a career in any engineering discipline, you'll generally need a degree.
The next thing to consider is being certified as a Professional Engineer. Doing this will require preparation, of course, followed by a certification exam.