Getting an airport bus to the eastern suburbs will be the easiest way. Getting a Taxi will be the most expensive way - I think you can hire a car for a day cheaper than the taxi ride.
Otherwise try Metlink as a public transport planner (I haven't used it, I just found it).
also look up Home - Airport Bus Eastside or Skybus Super Shuttle
For a single person, the bus is cheaper than Fuel, Tolls & Parking costs.

