I am sure that there are many sites and blogs that provide this information on the web, but thought I would like to add my thoughts based on my recent backpacking experience to this island nation.
Port of Entry
There is only one International airport in Sri Lanka, which is the ‘Bandaranayake’ airport, about 35 kms from Colombo. Currently, this is the only port of entry for international travellers. There is another international airport being planned on the South West coastal city of Hambantota, but locals tell me that this will take more than 10 years to get complete.
From the Colombo airport, one can take a bus, tuk-tuk (3 wheeler taxi) or a four wheeler taxi (cab, van) depending on budget and baggage size. Buses work out the cheapest, though slightly difficult if you are carrying a lot of baggage. There are AC and Non-AC buses (Bus No. 187) that connect the airport to the main city bus stand at Pettah. These buses run 24 hours a day and cost 50 LKR (Non-AC) and 130 LKR (AC) for the 60-90 minute journey depending on traffic. There are buses every 15 minutes during the day and the frequency drops to one every hour during the night. The airport bus stand, which is about 3 kilometres away from the airport is connected by regular free airport shuttle buses and tuk-tuks (cost LKR 100 for the one way trip). A Tuk-Tuk to the city would cost between LKR 800 and LKR 1500 depending on the time of commute. Night charges are higher. A 4 wheeler taxi would cost between LKR 1500 and LKR 2500 depending on time of commute. All mentioned prices are from the airport to Colombo Fort or Pettah, which is the city centre and houses the Colombo railway station and the main city bus stand (government and private).
Nearly the entire island nation of Sri Lanka is well connected by all-weather roads. This is also the fastest mode of commute. For luxury-oriented travellers, AC vans (Nissan Caravan, Toyota Hiace and lookalikes) are available at 30 LKR per kilometre. In addition, there is a driver fee of LKR 500 per day. These are the base rates, though the cost may vary with quality of vehicle and commission of travel agent.
For budget travellers, buses and trains are available. Most of the cities have private and government buses plying. The private ones are quicker, but cost slightly more than the government one. But, in principle, both of them are good. For longer journeys or commute between important cities, AC buses are available. All these buses start from the respective city bus stand. All notice boards in these bus stands are available in English too, apart from Sinhala and Tamil. To give you the idea of the cost, a private bus from Thissamaharama to Matara (140 kms or 3 hours) costs about LKR 115 per person. On the same lines, a private AC bus from Galle to Colombo (117 kms or 3 hours) costs about LKR 230 per person. Mostly, the buses are on time, though it would be best to keep a small tolerance.
In terms of train travel, the Sri Lankan railways, cover about 50% of the country. They are most efficient between Colombo and Kandy, Colombo and Galle and Colombo and Badulla as there are umpteen trains available every day with the option of AC, 1st class, 2nd class and 3rd class on these trains. The trains are comfortable, but are known to get delayed quite regularly. Currently, tickets cannot be booked online and one needs to go to the train station booking counter to book in advance. Advance bookings open for 14 days before the actual boarding date. As a thumb rule, 2nd class and 3rd class tickets are available on the day on the journey. However, first class and AC tickets get sold out quickly. The situation is much different during festivals and national holidays, when everyone is eager to visit their hometown.
The train from Colombo to Nanu Oya in the central highlands is quite popular with the tourists as it passes through tea estates, meanders across waterfalls, streams and hills. For such a train from Colombo to Nanu Oya, the 1st class observation car costs about LKR 750, the 2nd class about LKR 450 and 3rd class about LKR 230. As far as I remember, there are AC trains only between Colombo and Kandy, though I guess this will change pretty soon as upgrades are being made to the Sri Lankan train system.
For shorter inter-city travel, even the tuk tuk (3 wheeler taxi) is possible. Passengers would have to pay the entire round trip fare even for a one-way trip. Remember to bargain well with tuk tuk drivers.
For larger cities, buses are the best option. They are cheap, available in plenty and are efficient. For those who want to save on time, the tuk tuk is available at all corners, though you might have to bargain to get a good deal. Tuk Tuk drivers in Sri Lanka are known to stop by all tourists and enquire if they are interested in a ride. For luxury travellers, AC cars and vans are available, though, one will have to work out a daily package rate or get in touch with their hotel desk to get a good deal. This option is the most comfortable, though depletes your wallet pretty fast.
One can also hire rental cars and bikes. Luxury Rental car agencies like Malkey are actually more expensive than a chauffeured car/van, though CF Budget hires can work out slightly cheaper. Bicycles and motorcycles are also available on rent, though I have personally not given these a try. What I have heard from other travellers is that the state of these bikes leaves a lot to be desired.
If you are a good walker and can handle the sultry conditions (especially on the coastal side) of Sri Lanka, I would recommend ‘walking’ as a great mode of commute. Most of the cities are small in size, with the exception of Colombo and offer fantastic leisure walks while you admire the various locations on your travel map. In fact, Sri Lanka promotes walking through large and well laid out cobbled paths and a traffic system that gives preference to the walker than the automobile (something similar to the United States and most of Western Europe).