Qualifications
You'll likely need to get a graduate degree in finance or a related field (think: MBA), and it helps if you do so from a highly-esteemed university (source). And it doesn't matter if you esteem it—it should be generally regarded as a top-notch institution by education experts.
There are maybe ten schools that feed most of Wall Street. Exclusive club, yeah. As a general rule, if you don't see graduates of the school in question dressing almost entirely in argyle and smoking meerschaum pipes, it probably isn't Ivy League enough for you.