MRT, the Bangkok subway has two lines: the Blue Line, the first that was built and the Purple Line. Both line are connected at Tao Poon station. The Blue Line is the most interesting for tourist in Bangkok since it goes to Hua Lamphong, Bangkok main train station, Chinatown (Wat Mangkon station), Grand Palace, Wat Phra Kaew and Wat Pho (Sanam Chai station). Air conditioned like the BTS, it is a good option to get around and avoid the often congested traffic in the Thai capital. For single trips there are no tickets but black chips that can be purchased at vending machines which accept banknotes and coins. Counters are mainly used for information but can also sell chips. The price depends on the length of your trip. On vending machines by touching the screnn you can change the language and display a map of Blue Line or Purple Line to choose your destination and select it. The price will be determined based on your route. Then you have to put your coins or notes in the machine to get your black chip. Once your trip is complete, the exit portal will swallow your chip and put back into circulation so don't lose it. Note that since May 2022, you can use, Europay, Mastercard or Visa cards' contactless payment on MRT gates.
If you change network, you need to buy a new ticket. There is no common ticket, the three Bangkok metro networks are separate entities.
To go to Bangkok Northern Bus Terminal or Bangkok minivan hub, you must go to Chatuchak Park MRT station, then it will remain a fifteen-minute walk or 5 minutes taxi or motorcycle taxi trip to reach the Mochit Bus Terminal or Chatuchak Minibus Station. To take the train, stop at Hua Lamphoong station or Bang Sue since Bang Sue Grand Station is planned to fully replace Hua Lamphong at a date in 2022 that still needs to be chosen.
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 boats, 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.