First thing to do in any new country: learn the emergency number and write it down, because it differs by region and you do not want to look it up during a crisis. In an emergency anywhere, you call that number or go directly to a hospital emergency department, and treatment for life-threatening conditions is provided first with paperwork sorted later in most systems.
For urgent-but-not-emergency needs, countries offer different routes: walk-in clinics, after-hours doctor services, nurse hotlines, or hospital outpatient departments. Knowing which one your country uses saves hours of confusion, so ask colleagues or your insurer early.
On insurance compatibility, international health policies are accepted in most private hospitals, but the mechanics matter. Some hospitals bill your insurer directly if it is a recognised one, while others require you to pay upfront and claim reimbursement, which can mean fronting significant sums, so keep an emergency fund or credit capacity for this. Call your insurer's assistance line before or during any hospital visit if possible; they can direct you to network facilities and arrange guarantees of payment. Carry your policy card and the assistance number physically, not just in your phone.