Trincomalee is connected to Colombo by train — the journey takes roughly 7–8 hours through the North Central Province, passing through Habarana and the cultural triangle. The train is comfortable and the scenery through the dry zone is rewarding; the overnight train is an option if you want to arrive fresh.
Buses are faster for some routes — from Colombo the bus takes about 6 hours. From Kandy (about 5 hours) or Anuradhapura (about 3 hours) there are direct buses. From Batticaloa on the east coast it is a relatively easy 3-hour journey north.
Trincomalee has an airport used primarily by the military; there are no regular commercial flights at the time of writing, though this may change as tourist numbers increase.