Perth To/From Auckland
Air New Zealand are the only airline that does a direct flight, and there is only one per day.
Qantas and Jetstar have flights with stop overs in Melb and Syd which are generally cheaper than direct.
Ferry To/From Waiheke Island
The main ferry company is Fullers360 : www.fullers.co.nz/timetables-and-fares/?from=AUCK&to=WAIH
The Fullers ferries leave from Auckland City - Piers 11 & 12, Downtown Ferry Terminal, and arrive at Matiatia Terminal. The direct ferry takes around 40 mins each way, some have a stop over which adds 10 minutes travel time.
There are many car hire companies on the island. We highly recommend hiring a car to get the most out of the island. https://www.gorentals.co.nz/rental-car-locations/waiheke/
Waiheke doesn't have Uber, they have their own ride share company "RYDA". Download it before arriving!
There are taxis on the Island: +64 800 924 222.
All of the main roads across Waiheke are covered on the public bus network. They reach as far as the northern beaches and Rocky Bay (in the south), in addition to Onetangi Beach (in the east) and the Matiatia Ferry. Some of the buses even have cycle racks on the front, should you want to bike around the island too.