How and why did Captain Arthur Phillip come to Australia?

Captain Arthur Phillip was an ex-Royal Navy man with a distinguished record. Although he was in semi-retirement, he was interested in new challenges. Thus, when the British authorities were seeking someone to establish a convict colony in New South Wales, they saw Phillip as a most suitable candidate. In October 1786, Phillip was appointed Governor-designate of the proposed British penal colony of New South Wales. He had the military experience to also established the military colony to protect the East India Company trade as directed, and in doing so also preempted French intrusion into the South Pacific arena.

As for how he came to Australia - he came aboard a ship, as Captain of the First Fleet. This was the fleet of eleven ships which transported the convicts to Australia, along with the marines and officers.