Bangkok's Sky Train (BTS - Ekkamai). The cheapest, safest, and best way to get around the city. While in Bangkok I learned the BTS well. Because traffic can be terrible at certain times of the day, I found that a combination of the moto bikes, or tuks, and BTS work the best. Taxis are also nice because they are safe and metered.
Tip: If you can't explain where you want to go to a taxi, tuk, or moto bike driver, make sure you at least know what BTS stop is closest to your destination and tell them to go there. They'll know all the BTS stops. The BTS is the main vein of the city and runs right above Sukhumvit.