Bangkok buses are very heterogeneous. The colors, patterns, levels of modernity and comfort varie a lot from one line to another. Tickets can be purchased once on board to the attendant. The price depends on the distance that is why you need to make him or her understand where you intend to go.
The bus network consists in 108 lines and is impossible to summarize in a single map. So I created a small bus search engine to help you find the bus lines that serve the major Bangkok places and add the skytrain and subway map just in case. Note that there also are the BRT Buses in Bangkok.
The Bangkok Skytrain is called BTS. The trains have air condition and let you go over the heavy road traffic in the capital but you can not go everywhere even if connected to the Chao Phraya Express baots, it can let you go to major temples in Bangkok.
The Chao Phraya Express boats run regularly on the river running through Bangkok. They go to all monuments and interesting places on the river shores including Wat Phra Kaew, Wat Pho and Wat Arun, the three must see temples in Bangkok. Fare is cheap.
Taking the bus to get around is clearly not the easiest mean of transportation to use for a foreign tourist in Bangkok neither the fastest one but it's the cheapest one. Bangkok bus network is wide and you can go almost anywhere but just need to be patient.
Only Thai city for the moment to have a metro (there is metro project in Phuket), Bangkok is the city in Thailand that offers more choices of public or individual transport (metro, bus, boats, tuktuks...). No, there are not just tuk-tuks and pink taxis to get around Bangkok !