Clinical studies have persistently and reliably shown that anxiety and depression responds well to both psychological therapies (CBT, counselling, etc) and medication, but that a combination of the two is the single most effective. As a first line, however, psychological therapy may be successful without medication and this can be tried alone first, if the patient and their doctor feels it is safe to do so.
Other conditions have a different therapeutic profiles - for example OCD responds very well to medication, and people with drug addictions may or may not benefit from them.
What talking therapies are there?
There are a few types which vary in method and it is difficult to say who will respond well to one or the other.
CBT (Cognitive Behavioural Therapy) involves either one-on-one or group work in which the therapist will help to understand and change thought patterns and behaviours which are harmful. Common ways they do this is helping people to recognise their triggers, their early warning signs, and to prevent escalation of an emotional state before it takes over. This can be very useful for habits, phobias and social anxiety. It is also often used with depression.
DBT (Dialectical Behavior Therapy) is very similar, and employs techniques such as mindfulness, distress tolerance and acceptance to help people to change their behaviours into more productive ways of coping. This can be particularly helpful in suicidal thoughts, self-harm, substance abuse and personality disorders. It is very new and its efficacy is still under evaluation.
Counselling is often used for acute situations such as grief, stress and crisis situations. This can be short term or slightly longer and gives the client someone to talk to and explore their feelings with when they are struggling to cope with or understand them. Most people benefit from counselling (and some people think everybody should have counselling!) even if they are entirely functional and lead a subjectively "normal" life.
Psychotherapy is a more intense form of counselling. This involves having an in depth relationship with a therapist, which develops over months or years. Often the client will see the therapist once or twice a week. It is very helpful for lifelong behavioural or personality traits which are causing significant distress.
Does medication help?
There are many types of anti-depressant medication which studies have shown to be most effective in treating depression.
SSRIs (Selective Serotonin Reuptake Inhibitor) and SNRIs (Serotonin and Norepinephrine Reuptake Inhibitor) stop serotonin, a neurotransmitter that helps neurons to fire and carry messages around the brain, from being reabsorbed for a period of time. This means that neurons fire more easily, carrying positive messages around the brain more often than they did without taking it. This doesn't cause any direct effect straight away but after a period of time, usually a few weeks or months, it means that new neurons grow and this change can become pernanent. It means that the patient is able to think more positively and for more pleasant thoughts and confident thoughts to occur more easily. It helps the person to think more clearly and clears away that helpless feeling.
Mirtazepine (Avanza) works very similarly to an SNRI.
Other classes of antidepressant include TCAs (Tricyclic Antidepressants) and MAOIs (Mono-Amine Oxidase Inhibitors). They are often second or third line after SSRIs (unless you cannot take an SSRI for some reason). If you are interested in these medications, consult your doctor.
What about Bipolar Disorder and Schizophrenia?
People who have experienced these conditions often will need to work with a psychiatrist to find a medication regimen that works for them. They may need to be on some form of medication for the rest of their life. Typically, both conditions respond well to antipsychotic medication. People with bipolar disorder will often need mood stabilisers to ensure they don't become too manic or too depressed.