The official language of Thailand is Thai (ภาษาไทย). It is a tonal language, so it can be difficult for native English speakers to learn quickly, but everyone will appreciate any attempt you make. Thai is a language with many dialects, though the Bangkok dialect, also known as Central Thai, is used as the standard and is taught in all schools. Language schools can be found in all larger Thai cities, including Bangkok and Phuket.
In the Muslim-dominated south, dialects of Malay that are largely incomprehensible to speakers of standard Malay/Indonesian are spoken. Various dialects of Chinese are spoken by the ethnic Chinese community, with Teochew being the dominant dialect in Bangkok's Chinatown. Down south in Hat Yai, Hokkien is also widely understood due to the large number of tourists from Penang. The eastern Isaan dialects are closely related to Lao and there are dozens of small language groups in the tribal areas of the north, some so remote that Thai speakers are few and far between.
Public signage is generally bilingual, written in both Thai and English. There is also some prevalence of Japanese and Chinese signs. Where there is English, it will usually be fairly phonetic - for example "Sawatdee" (meaning hello) is pronounced just as it reads: sa-wat-dee. There is no universal agreement on how to transcribe Thai letters into English, so Khao San Road for example is also commonly spelled Kao Sarn, Kao Sahn, Khao San, Koh Saan, Khaosan, and many other variations. Maps with names in both Thai and English make it easier for locals to try and help you.
Most Thais learn English in school, and most younger upper and middle class Thais, as well as many people working in the service industry in Bangkok and other touristy areas, have a basic grasp of the language. Outside of that, English proficiency is generally poor to non-existent. Most "front desk" people in the travel industry speak at least enough English to communicate, and many are relatively fluent; some also speak one or more other languages popular with their clientèle, such as Chinese, Japanese, German, etc.
Many Thais have trouble pronouncing the consonant clusters of the English language. Common confusion comes from the fact that Thais often pronounce "twenty" as "TEH-wen-ty", making it sound like they're saying "seventy". Therefore it is a good idea to make use of the calculators that street vendors may offer you to avoid confusion about prices offered when buying goods.