Puli is easiest by bus. Frequent buses run from Taichung to Puli, and onward buses continue to Sun Moon Lake. Direct buses from Taipei also serve Puli, but Taichung is the more flexible rail-and-bus route.
Once in town, check the bus timing before heading to outlying sights. Taxis are common around the bus station and are often the simplest way to combine the monastery, paper mill, and Paper Dome in one day.