From Taipei:

The Gwo Gwuang Bus company has  busses to Puli  every half  hour or  hour.  They are  located  behind  the Taipei Train Station.

Or  you can take the train or bus to Taichung. Then take another bus  from the train station. Travel  time is  about 4 hours.

Driving?     Take  the  National Highway  number  3  to the Tsao Tsun  exit.  Follow the  signs to Puli.

From Taichung:

Many bus companies  operate directly to Puli from Chienkuo Road arriving in about 1 hour 20 minutes.

Driving?     Take  the  National Highway number  3  to the Tsao Tsun  exit.  Follow the  signs to Puli.

Flying?    DON'T  BE  A FOOL!!!