Psychiatry is the medical discipline associated with working with a mind. Some psychiatrists are also psychotherapeutic trained. As psychiatrists are medically trained they are likely to use a medical model for intervention, are allowed to prescribe, although not all psychiatrists work entirely within this frame. Please look at the biographies, psychiatrists to see their interest.
Psychology is the study of mind, brain and behaviour. Psychology can be studied in many forms including: clinical, forensic, occupational, experimental and others. They may have different approaches but generally start from the need to understand human behaviour (and in some cases animal behaviour). Psychology differs from psychiatry in that while psychologists may or may not be Drs, as in having PhDs, psychiatrists are medically trained and are able to prescribe medication. A psychotherapist will have areas of overlap with psychology but they do not have to have a degree in psychology and therefore some of the training will be different.
The approach of a psychologist who offers therapy is to assess the issue or issues causing distress or dysfunction and then offer a therapeutic approach in which they are trained. This can be psychoanalytic, psychodynamic, cognitive, behavioural, or a combination in which case the therapy may be called integrative.