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.
There are several private bus services operating from Colombo to Jaffna, cost varies from 900 Rupees onwards for a person. The drive takes half a day to complete (9 hours +) following the A9 motorway which runs through the middle of Sri-Lanka. From/to Vavuniya the journey costs approximately 180LKR by private bus and takes around 3.5 - 4 hours. Currently the road is being upgraded causing slight delays. Vavuniya has good connections to other parts of the Central North. Alternatively buses pass through Anuradhapura (1-1&1/2 hours south) however Vavuniya to Jaffna buses leave regularly throughout the day so any waiting in Vavuniya should be minimal.
Travellers are advised that bus drivers may frequently switch off air conditioning to save energy and petrol. However, this causes the air to warm up and be stale in the enclosed bus. Unfortunately, complaining does little. Hence do take precautions.
There are four trains a day to Jaffna from Colombo theoretically taking 6-8 hours (count on 8-10+). Observation (LKR 1,100 one way), 1st and 2nd class tickets may be booked up to 45 days in advance but these go quickly so book well in advance. Unfortunately, tickets need to be booked in person at Colombo Fort or Jaffna station. No on-line booking facility available as of March 2015.
Once in Jaffna there are several modes of transport.
By auto (tuk-tuk)
these are three wheelers which are very common in south east asian countries. These are the quickest and probably the cheapest way to get around to places.
Public transport system available in Jaffna are the buses. See http://jaffnavisit.com/category/bus-root/ for route maps.
These are private hire mini-vans, best if you need transportation for the whole day.
The locals get around on cycles and Mopeds, and (fairly ropey) push-bikes are available for a few hundreds rupees per day at some guesthouses. One can cycle out to the islands along the quiet (ish) roads. There are a good collection of shops (including an ice-cream shop) in Velanai but be warned the roads are almost completely shade-free; so be prepared for a lot of sun although of course it is a very easy flat cycle. Keep watch for war-damaged buildings and note that the beaches on the islands (including 'Chaddy beach') are not really worth considering as swim-worthy by Sri Lankan standards.
Nallur Temple A bustling and beautiful temple which is worth a look. Note that you must be barefoot to walk the temple grounds and men will need to remove their shirts to enter the temple. Free entry.
Selva Sannithi Temple
Nagapoosani Temple (Nainatheevu)
Sri Naga Vihara Temple
vaddu kannaki amman temple -vaddukoddai
Point Pedro Take a bus from the central bus station (Rs. 68 one-way) to Sri Lanka's most northern point. The journey will take an hour to the town of Point Pedro from which it is a 5 minute walk north to the Point Pedro sign and a small beach. Worth a half-day trip. The red buses marked Point Pedro depart every hour from Jaffna.
There isn't a lot to do on Jaffna unless you arrive at festival times. Nallur Kovil Thiruvizha (festival) is the biggest event in the Jaffna calendar when all the faithful come home to pray.
Water isn't good because of mineral content. The local brew is toddy, from the coconut or the palmyrah tree. Toddy from the palmyrah tree is sweeter.
Buses depart to various places around Sri Lanka, including Mannar, Batticoloa and back to Colombo. A full timetable is printed at the enquiries desk at Jaffna bus station, though tickets can only usually be bought on the bus on the day of travel.
Kandy - public bus 8 hours Rs400 - there are regular public (red) bus towards Kandy during the day. So don't believe in any of those people telling you that the bus has departed and asking you to ride on his vehicle instead.
Trincomalee - public bus 88 departs at 04.00, 04.15, 06.00, 07.00, 11.00, 12.00, 14.15, 16.15 and 19.00, costing around Rs. 250.