The usual way of seeking protection is to come to a country and ask for protection. This is commonly called ‘seeking asylum’, and people who come this way are often called ‘asylum seekers’. This generally means that they have not yet had their claims to be a refugee formally determined.
In Australia, ‘seeking asylum’ is often seen as being the ‘wrong’ way to come, and the ‘right’ way is to wait in a queue and be selected by UNHCR for resettlement. In fact, seeking asylum is the way most people get protection in the world, and is the way that is protected by the Refugee Convention.