Psychotherapist is a generic term for someone who provides psychological therapy. It does not by itself describe a particular mental health professional or a particular approach to therapy.
A Psychoanalyst is a mental health professional who uses Freud's psychoanalytic therapy to treat emotional problems. A traditional psychoanalyst does fairly intensive treatment that tends to take a long period of time to take effect. There is some controversy over the effectiveness of psychoanalytic treatment, and what are the appropriate types of problems for psychoanalytic treatment.
A psychologist is a mental health professional that is trained in psychology. Psychologists who provide treatment - clinical psychologists, counseling psychologists, and school psychologists, for example - have training in psychological foundations, clinical assessment, and psychotherapy and counseling. They do talk therapy as well as do psychological testing. They may use a variety of different treatment approaches, including psychoanalysis, cognitive therapy, behavioral therapy, and other types.
A psychiatrist, by the way, is a medical doctor who specializes in treating emotional problems. They can do talk therapy and can also prescribe medication and admit persons to hospitals where needed. Because of their training they tend to work with persons with serious mental illnesses and issues where there is possible medical complications.
A few things to remember when selecting a therapist. First make sure that they hold a license to practice their specialty (psychology, counseling, social work, or psychiatry). All psychotherapists typically do talk therapy, although each may have a particular approach that they use. Make sure that the professional that you go to has experience and training in the problem area with which you want help. Psychotherapy is a relationship with someone, so how well your personality and the personality of your therapist fit make a difference. Some folks find that they have to shop around to find a therapist that they feel they click with. For more information on selecting a therapist and on psychological problems go to the American Psychological Association website at http://www.apahelpcenter.org/. Very good articles on choosing a therapist, when you need help, and other topics are available on the North Carolina Psychological Association website at http://www.ncpsychology.org/html/GeneralPublic.htm
As far as addictions go, you should find someone who specifically works with addictions. Typically that isn't a psychoanalyst. Addictions treatment often includes the use of 12 step type group support programs.