We went this tour 23-25 of December 2015 by intercity AC train which leaves Colombo Fort at 5.35am and reaches Jaffna at about 12.15pm. Seats can be reserved prior to 45days. Government servants eligible for 1st class warrents can also reserve this train.
Try to reserve as early as possible if you plan to travel in high season. Train journey is quick and really comfortable.