The first is Cognitive Behavioral Therapy, which identifies in people negative thought patterns that are adversely effecting the overall mood of the person. The way it ends up working on the long run is that the therapist works with you to develop skills to change these thought patterns into healthier ones. The second is Pyschodynamic Therapy. This is for people whose depression comes from a long standing emotional cause. This is what people typically think of when they think of psychotherapy as it helps you understand and cope with problems and unresolved problems in your past that may be contributing to your depression. The third is Interpersonal Therapy. This approach has more to do with communication so that you can build confidence in yourself and see relationships around you in healthier ways.
There are multiple ways to have therapy, including going with a friend/family member, or alone, or to a group session. You'll want to do your research and meet each potential therapist until you find one you think is going to be right for you. They can also help you decide what kind of sessions you'd like and what might best serve you.