A counsellor (therapist/psychotherapist) is someone who has at least Masters-level of education and training in counselling psychology. Their role is broad and diverse, where they are able to deal with issues ranging from day-to-day challenges, to suicidality, to post-traumatic stress disorder. Some counsellors can really specialize in certain modalities (eg. CBT) or in a population (eg. at-risk youth).
Generally speaking, a psychologist (or clinical psychologist, registered psychologist) is someone who has a PhD in psychology. They can be an academic who conducts research, a clinician who provides psychological diagnoses and assessments, provide therapy, or any combination of the above. Registered psychologists (that is to say, clinical psychologists) tend to focus their training and area of practice, rather than take on a broader array of issues, as a counsellor would.
A psychiatrist is a medical doctor who has training in diagnosing mental illness and prescribing psychiatric medications, such as anti-depressants or mood stabilizers. Their training for providing talk therapy may vary, as this may not have been a requirement for their educational background.