Taxis are the most common, but there are many types of taxis. There is the common taxi that uses a meter and are usually yellow or pink in color. The metered fare is resonable and they will often try to negotiate a flate rate before getting the ride. The rate is almost always way too high. Then there is the tuktuk. Said as it's spelled. The tuktuk is a three wheeled modified motorcycle, that runs on natural gas, making them a bit loud. The tuktuk can be expensive but pricing is negotiable. The motorcycle taxi is a quick alternative for getting short distances around the city but requires a bit of courage, especially during rush hour. While I often take a motorcycle in the morning to the office, it took several years to build the courage.
Vans are a great alternative to buses but they do not operate on a given schedule. When they fill, they leave. They are usually fastest if they are going where you want to go and can be comfortable but are crowded. The tour agencies often use vans as an alternative for smaller groups. Vans usually operate at a competitive price and there are many van companies so if you can, shop around. The main hub in Bangkok to catch a van is Victory Monument Circle.
Thailand Trains - Three are three types, the MRT (Subway), BTS (elevated metro train) the airport link and the SRT (State Railway of Thailand). The MRT, BTS and airport link are great for getting around Bangkok and are fairly inexpensive. Here is a link to a pretty good system map.
You can use the Google Map below to help plan your trip and use the links in your smart phone while you are here:
View Bangkok Destinations in a larger map