If your doctor refers you to hospital for treatment, you will usually be given an appointment to see a specialist doctor. Depending on the medical problem, you may be treated as an in-patient (where you are admitted to a ward and stay there overnight or longer) or as an outpatient (where you visit the hospital for an appointment but do not stay overnight or longer). If you think you need to see a specialist, you should approach your own doctor first and ask her or him to refer you.
If you are referred to hospital by your doctor, you will not need to pay for anything other than prescriptions. There are often long waiting lists for hospital appointments and procedures, so unless you need treatment urgently, you may want to wait to be treated on your return to your own country.
Please note that if you are not from an EU/EEA country and are on a programme of study of less than six months you are strongly advised to take out personal medical insurance, as it is highly unlikely that you will receive free hospital treatment unless you are involved in an accident or emergency, or because you suffer from a particular communicable disease such as malaria or tuberculosis.