BMTA run the city busses in Bangkok.
Air con busses cost just over 10 bath, while busses without air conditioning will be a bit cheaper.
Bangkok has three main bus terminals for long distance travel, depending (roughly) on what direction you need to travel (north, east or south).
This is the biggest one in Bangkok, and has good connections with North, Central, Eastern and North Eastern areas of the city, and nearby countries.
There are bus routes to Chiang Rai, Uttaradit, Chiang Mai, Lampang and many more. You can also go to Laos and Cambodia from Mo Chit Bus Terminal
There are over 50 ticket counters, and you can buy tickets there on the day.
The bus station is close to the Mo Chit BTS Skytrain station. It is also close to the Chatuchak Weekend Market (8,000 market stalls at the weekend - the biggest in Thailand).
This coach station has routes to the east coast of Thailand including Pattaya and Rayong).
This bus station has routes for southern Thailand, including Phuket, Krabi and Ko Samui.