From the airport to UH
The airport flyer will take you all the way from Wellington airport to Upper Hutt train station for $14.50.
It is comfortable and has racks for baggage. Departures are reasonably frequent.
See the website for timetables. It takes around 90 minutes and there are limited stops between Upper Hutt and Wellington.
Update Nov. 2012, looks like the service to UH will be discontinued and will only go as far as Queensgate shopping centre in Lower Hutt, but it is possible to change buses there for Upper Hutt,
Getting to UH
The train goes right out to Upper Hutt from Wellington on the Hutt Valley line. Takes 40-45 minutes and costs $8.50 one-way. Frequencies range from every 20 minutes in peak time to 1 hour in late evenings.