The official language of Myanmar is Burmese (known by the government as Myanmar). A majority of Burmese pronunciation is derived from the ancient language of Pali (at the time of the Buddha), but the language is a Sino-Tibetan language related to Chinese and hence tonal (word pitch matters) and analytic (most words are one syllable long). It is written using the Burmese script, based on the ancient Pali script. Bilingual signs (English and Burmese) are available in most tourist spots. Numbers often are also written in Burmese script.
There are also many other ethnic groups in Myanmar such as the Mon, Shan, Pa-O and many others who continue to speak their own languages. There is also a sizeable ethnic Chinese community mostly of Yunnan descent, most visible in the city of Mandalay, and many of whom speak Mandarin. Some areas are also home to various ethnic Indian communities who continue to speak various Indian languages. However, with the exception of the elderly, it is rare to find any locals who do not speak Burmese.
Myanmar is a former British colony, and as a result - and because English is still being taught in kindergartens and primary schools - many Burmese understand at least some rudimentary English. Most well-educated upper class Burmese will be fluent in English, while in the main cities like Yangon and Mandalay, many locals will know enough English for basic communication. In fact, you may find more English spoken in Myanmar than in Thailand.