There is limited counselling and psychotherapy available through the public health system, and where it is available it is usually only available for people meeting criteria for a serious mental illness. See your doctor to find out if you can receive treatment through the public health system.
Most people will receive their counselling from a private practitioner or a charitable agency. Fees are usually paid at the time of each session and vary depending on such things as location, training, and experience. It is your right to ask your counsellor about their charges and cancellation policy before you start counselling.
Various organisations subsidise or fully fund counselling for specific purposes. This is referred to as "third party funding". Third party funders each have their own eligibility criteria, assessment and reporting procedures for both clients and counsellors. They also have their own criteria for deciding how many counsellors they need to have to provide counselling for them.