You can get a train from Colombo, Jaffna for the trains timetable click here
runs 3 times a day and ends at Kankesanthurai. There is also a night train departs at 20:30 arrives Jaffna at 05:10.
Bus No: 87 from Colombo Fort - Jaffna
Colombo Fort - Chilaw - Puttalam - Anuradhapura
Overnight A/C bus booking info