Fujinomiya is located on the JR Minobu Line, linking Fuji on the JR Tokaido Line with Kofu on the JR Chuo Line.
There are a few ways to get to Fujinomiya from Tokyo, but the fastest method is to use the Tokaido route from Tokyo: to take a Tokaido Shinkansen Kodama train to Mishima, and change there for a Shizuoka-bound JR Tokaido Line local train. At Fuji station, you need to change again to the JR Minobu Line for the final run to Fujinomiya. This whole process will take about two hours with good connections at a cost of ¥4710.
Even substituting the Kodama journey with Tokaido Line local trains, the trip still takes about three hours from Tokyo if the connections are good, at a cost of ¥2520