1. You cannot visit a specialist or go to the hospital directly. You need to visit a GP (General Practitioner - طبيب عام).
GPs are available everywhere. They are supposed to take care of ALL of your medical needs, except teeth. You and all your family members should (but not a must) go to the same GP all the time. He/she would develop (over the years) complete history of you and your family members. If the GP does "Bulk Billing," his/her fees are 100% covered by Medicare (you don't pay anything.) If not, you have to pay his/her fees and claim part of it from Medicare. They will advise you about the procedure to do so.
Some GPs can be visited by walking in (first come, first serve basis), while others require an appointment.
Some GPs are much better than others. You need to ask around (your neighbours, parents of your children at school, etc.) about good GPs in your area.
2. If you need blood/urine/stool tests or x-ray, the GP can request them. Most of these are 100% covered by Medicare. So, you don't have to pay anything.
3. If you need medication, the doctor would write a prescription for you (روشتة). The government has a scheme called PBS. If the medicine you need is on the PBS list (most medicines are), you need to pay only $3x of the cost of the medicine. I am not sure if it is $33 or $35; something like this. So, if it costs $235, you pay only $3x. If it costs $20, you pay only $20.
4. If you have a pension (or a health care) card, you pay only around $6, instead of about $35. This card is provided by Centrelink (Human Services) to people having a low income. You need to check their website for more details.
5. If your problem needs a specialist's consultation, the GP will give you a "referral letter" to the specialist. You need to call the specialist for an appointment. Specialists' fees are costly (sometimes more than $300). Some charge more than others. For most illnesses, Medicare reimburses (returns) you part of what you paid to the specialist, e,g, $70. When you make an appointment with the specialist, you can ask about his/her fees and the amount, which Medicare reimburses you with.
If you have private health insurance, the insurance Co might reimburse you some additional amount to the Medicare amount - depending on your insurance plan.
6. If you need admission to a hospital (e.g. for an operation), the cost of most operations is covered by Medicare. However, for some operations, there is a long waiting list (up to a year in NSW).
If you have private health insurance, you can get the operation done faster in private hospitals, and you can get special services, like a private room. However, you might need to pay a "gap," which is the difference between what the private health insurance policy covers and the actual cost of the service.
7. If you need an ambulance, you pay $500 for it (in NSW)! I think this is different in the other states. If you have a pension card, you don't pay for an ambulance. In most cases, private health insurance covers the cost of an ambulance. You do NOT need to pay for the ambulance in advance. You will be billed at a later date.
8. Some medicines are categorised as "over the counter", which means you can buy them without a prescription. Pension (or health care card) discounts do NOT apply to these medicines.
Other medicines need a prescription. These are hidden behind the pharmacist. You can only get them if you have a prescription.
9. Generally speaking, every health service has an "item number." Specialists and health providers can charge whatever fees they think is appropriate. However, Medicare has a limit on what they cover. You would pay for the service, and then claim some/all of the fees from Medicare.
Please, visit the Department of Human Services website for more details (https://www.humanservices.gov.au/customer/dhs/medicare), and to get a Medicare card.