Cheapest:
Fly to Christchurch and hitch. Lots of climber folk from Christchurch head to Paynes over summer, so post on http://www.mojozone.co.nz and you may be able to hook up with someone. Other good reason to go via Christchurch is it puts you closer to Castle Hill if you haven't been and are keen on bouldering (100km away, easy hitching as on the main route to the West Coast). If you go to Castle Hill you may also be able to hook up with others road tripping around and get a ride to Paynes (tho this is probably a long shot).
Bus would be the next cheapest option - look up Atomic Shuttles but there are heaps of backpacker bus services as Neil rightly points out. Motueka is the closest big town and I'm sure there are shuttles that go 'over the hill' from Motueka via Takaka (right by Paynes Ford in fact) coz the Abel Tasman National Park spreads around the coast from Motueka to Pohara(ish) - Google 'Motueka Takaka shuttle' should get you going.
At Paynes:
Stay at Hangdog, and you can access all the Paynes Ford crags on foot no problem (5 minutes walk to nearest crag, and they stretch off, furthest is about a 45min walk). There are other crags at Pohara on the coast (about 10km away) but you should be able to hook up with others at Hangdog if you are keen to get out there.
I doubt anyone but private charters fly to Takaka - it's only slightly bigger than Natimuk!