Simply jump on the Wairarapa train in Wellington and catch a connecting bus to Greytown. Check out the Wellington to Wairarapa timetable here.
To get to Greytown by train during the week, hop off the train at Woodside Station (it's 5km out of town) and board the bus which meets all weekday trains (except the late train on Fridays). It will whisk you straight to Main Street, Greytown.
To get to Greytown by train on a Saturday, you’ll actually need to get off the train at Featherston Station. This arrives at 10.46am. You hop on the route 200 bus waiting at the station at 10.58am which takes you to Main Street Greytown. You’ll arrive there at 11.15am. To get back to Featherston to catch the train back to Wellington on weekend afternoons catch the route 200 bus at 4.55pm outside St Johns Hall (opposite The Hub) on Main Street, (Greytown Bus Stop 1822 - Main Street near 74). This will get you to Featherston Station at 5.10pm in time for the train. You'll return to Wellington at 6.25pm.
To get to Greytown on a Sunday - while KiwiRail does infrastructure improvements and essential track maintenance, Sunday services from Wellington will be via bus not train. The bus leaves Wellington Railway Station at 9.25am and arrives at Greytown at 10.54am . You'll be able to get off right in town at Bus Stop 1822 Greytown - Main Street near 74. To return to Wellington catch up bus at this same stop at 5.17pm. You'll return to Wellington at 6.46pm
Or bring your bike on the train and cycle into town along the pretty Woodside Trail. Just get to the station early at peak commuter times (4.25pm and 5.30pm) as the bike carriage can fill up fast.