Mt. Haguro is located in the area of Tsuruoka City, in Yamagata Prefecture.
If you are going to use public transportation, first you have to reach Tsuruoka Station.
You can take a Shinkansen bullet train running on the Jōetsu Shinkansen from Tōkyō Station and so reach Niigata Station; here you have to take a Uetsu Line local train and get off at Tsuruoka Station (it may need you to change train once or twice along the way). The journey takes about 4 and a half hours, and from Niigata Station and Tsuruoka Station you will be able to enjoy nice views on Sea of Japan.
At Tōkyō Station you can also get on the Yamagata Shinkansen heading to Shinjō Station; you then transfer on the Rikū West Line and reach Amarume Station, where you can take the aforementioned Uetsu Line (this time, southbound) and arrive at Tsuruoka Station. This journey takes about 4 hours, and passes throughout the inner area of Tōhoku Region.
Both these routes don’t need any extra fee if you use a Japan Rail Pass, including its East Japan (Tōhoku) limited version, and the round trip can nearly pay off the price of the weekly pass.
If you are travelling by plane, Shōnai Airport is linked to the main Japanese airports, including Tokyo Haneda with direct flights. The price of the flight may be a bit costy, but from Tokyo you can reach Yamagata in less 1 hour. At the airport you will find a limousine bus service (usually synchronized with the arriving flights) heading to Tsuruoka Bus Terminal, located a few meters west from the train station.
At the Tsuruoka Bus Terminal you can catch a bus heading to Mount Haguro.
Arrived a the foot of Mount Haguro you can reach the summit walking on a 1.8 km long stone staircase realized in 1648, during the Edo period. Otherwise, if you come by car, or you have reded one, you can drive on a handy paved toll road leading near the summit.