One of the cheapest ways to travel around Sri Lanka is by train. The tickets are incredibly cheap. The big problem is that the train network may not go to where you want to travel to. If you are on a budget that means going by bus.
Sri Lanka private company operated Lanka Ashok Leyland Bus
The bus network is quite extensive but they are hot, sweaty, smelly, dirty and over crowded. The pretty coloured busses are privately owned where as the unattractive dark red busses are government run. All the intercity tickets are reasonably priced.
You may be lucky and strike up some interesting conversations with local travellers who want to try out their English. A good conversation topic is cricket. Cricket is a religion in Sri Lanka. Even if you know nothing about the sport ask about the rules of the game and why it is so important.
You will find both private and government Central Transport Board CTB buses operating from the same bus station. Most now have their destination printed in English on a board at the front of the bus. If you are confused seek out a fellow passenger who has a good understanding of English and ask for their help.
Sri Lanka Government operated Bus
Most tickets are purchased from the driver but at some of the bigger bus stations their may be a ticket booth. If you have a large rucksack or suitcase you have a problem. These buses are designed for local transport not tourists. There is no provision made for tourists. The best advice is to buy an additional ticket so you can use a seat for your stuff.
Okay you are tourists and you want to see the countryside but do not sit in the front two seats unless your head is shaved and you only wear orange bed sheets. These are reserved for Buddhist monks. To guarantee a seat get to the bus station early and try to start your journey at the beginning of the route.
Check the internet for bus routes prior to arriving in Sri Lanka, There are a few air conditioned busses being introduced to Sri Lankan inter city bus routes. They are more expensive and seats can be reserved.
Sri Lanka private company operated Lanka Ashok Leyland Bus in Kandy