Then, you will probably prefer quieter and more corfortables or with air condition mean of transportation and opt for taxis which are gennerally contrary to popular belief cheaper than tuk-tuks. Despite the name tuk tuk in Thai meaning cheap. Tuk-tuks have no meter, you have to negotiate the fare before taking them. And do not hesitate to haggle, it's part of the game !
Besides that, the big majority of tuk tuk drivers is honest even if they will probably charge you a little more than a Thai. But don't be too trustful especially near the tourist areas.
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 !