Qualifications
You'll need a license. And for that, you will need—duh, duh, duh—a Bachelor of Architecture degree, which is usually a five-year program (source). If you want to take a crack at the big, important (ultra-well-paying) jobs, be prepared to spend another several years to get your masters and then some.
Want to do underwater bridge bays? You'll likely need some schmancy PhD in the subject to get real work. You'll also need to have a brain that works both the right and left sides pretty well—you have to be a math and sciences dreamer, but at the same time you need to be pretty creative and inventive.
Also, be prepared to intern for a while before being able to design anything on your own. You'll need to prove first that you're not going to do anything crazy, like design bathrooms with chimneys.