Qualifications
Graduate programs are competitive. Certain universities require applicants to have an undergraduate degree in psychology. Other programs may accept undergraduate degrees in statistics, social sciences, biology, or mathematics as long as you have some course work completed in psychology.
Those who want to become a psychologist must get a doctoral degree, which takes roughly five years to achieve. Graduate students earning a PhD take courses in research design, quantitative experimental methods, and computer-based analysis. In addition, those going to the research fields must complete a dissertation (source). A dissertation is not, as some may think, the preparing of a truly delicious baked good, although bribing your professor with a piping hot Dutch apple pie might not hurt.
People earning a Doctor of Psychology degree, or Psy.D., learn behavioral science and scientific methods. Students focus on diagnosing and treating mental illness. In addition to completing a dissertation, Psy.D. students focus on examinations and practical work. Once they've graduated, they must obtain a license in order to accept patients. Licensing requirements differ from state to state (source).
Generally, counseling and clinical psychologists must have one to two years of experience and pass an exam before the state will grant them a license to see patients. Technically, they can see patients before they're licensed. They just can't talk to them or communicate any advice or analysis via blinking or Morse code. Best to just get licensed so you can be of optimal use to them.