Twenty towns in Thailand have an airport with at least one connection to Bangkok but not always daily flights. To go to the Thai islands, there are ferry companies or speedboats, sometimes local or longtails boats for short distances.
For transport in Bangkok, besides the famous tuk-tuks and multicolored taxis, you have several public types of transport: metros, Skytrain, buses, Chao Phraya Express boats or boats on the khlongs, the small water canals running through the city. The metro network is extending a lot lately..
The atmosphere of Thailand night trains is nice and quite cofortable for a cheap price. For the price of a cheap hotel night you have a night sleep and a transport. To be sure to get a sleeper, it's recommended to book your tickets in advance via booking websites like 12Go (or SRT official website).
Khao San Road is known as the backpacker's area in Bangkok. Travel agencies and transportation companies offer bus or ferry + bus packages from Khao San Road to the popular Thai islands like Koh Tao, Koh Samui, Koh Phangan... but also to other destinations in the country.
There are direct buses from Bangkok to Phnom Penh or Sieam Reap (the city near Angkor) in Cambodia with border crossing included in the trip. Buses depart from Mo Chit Northern Bangkok BUS Terminal. The number of seats is limited so it is better to book in advance on 12Go.
If you prefer to organize your trip and book your train tickets before departure, know that this is possible via the website12go that I personnaly tested and validated. Advance booking is especially recommended for sleepers in night trains but can also be a good idea for some super Express trains.