I go to Fulong quite often from Taipei.
Take the MRT to Taipei Main Station. Follow the signs to get to the TRA (Taiwan Railway Association) where you can purchase a train ticket to Fulong. If it’s the weekend, however, you may have a hard time getting a seat (you can always get a non-reserved ticket and chance standing the entire way).
You can also take the bus, which will guarantee you a seat. Kuo Kuang Bus#1811/1812 (國光客運, also called King Bus) goes between Taipei and Fulong. Catch the bus at Taipei West Bus Station Terminal A.
How to get to Taipei West Bus Station Terminal A: Once you exit the MRT at Taipei Main Station, look at the signs and maps on the walls, and look for Station Front Metro Mall and the “Z” exits. Make your way toward the mall and Z exits. At exit Z3, go up some stairs to ground level and you’ll be right at the Taipei West Bus Station Terminal A. This site even has photos to guide you: http://taipeitoairport.blogspot.tw/2012/05/best-way-to-get-to-taoyuan-airport-from.html. When you arrive in Fulong you’ll exit at a huge parking lot with a visitor’s center.
Hope this helps. By the way, you aren’t a useless foreigner 