Kinkasan being an island, you'll have to take a ferry at some point, so the main question is choosing the ferry terminal.
By train
By train
If traveling by train from Sendai, take the JR Senseki line to Ishinomaki, then change to the JR Ishinomaki line for Onagawa. From here, you can take a 35-minute ferry to Kinkasan. Ferries travel every 2 hours or so and cost ¥1,600 one way, ¥3,040 return.
By bus
By bus
Alternatively, you can take a 90-minute bus from Ishinomaki to the whaling town of Ayukawa, from where ferries ply to Kinkasan in 20 minutes ¥900. Services from here are more frequent, as often as every half hour in season with two competing operators.