By train
Before the escalation of the war there was a train service running from Colombo to Jaffna but now it only runs half way to Vavuniya from where you will have to get a bus towards Jaffna.
By plane
Jaffna is the northern capital and has an airport based in Palali. Due to the current circumstances there are no international flights to Palali. To get to Jaffna one must fly into Colombo the southern capital and get a domestic flight to Palali.
There is air service to and from Colombo, provided by the national airline Sri Lankan Airlines. Flights are available from origins throughout Europe, United States, Southeast Asia, China, Japan, the Middle East, India, and Pakistan. Other airlines, include Qatar Airlines and Emirates. Colombo's international airport is at Katunayake.