You can take the local bus from Chang Puak bus station in northern Chiang Mai. Fang is 152km from Chiang Mai and it takes about 3 hours to get there by local bus. A ticket costs 80 Baht. Halfway the bus stops for a leak and a snack.
From the north, Thaton is about 40 minutes away by songthaew, with Chiang Rai another 3 hours away.