Sinhalese is the most commonly spoken language in Sri Lanka which is spoken by about 75% of the population while Tamil is spoken by almost the rest. English is popular as a second language and most people understand at least the basic English terms. So travelers who speak English will have virtually no trouble communicating in Sri Lanka. Especially those who engaged in tourism and related occupations almost always possess at least basic English conversation skills. So you can expect most hotels, drivers, guides to speak English while anyone you meet in the street understands basic English terms.
If you need to ask for some information from locals it is totally acceptable to use English. If you keep it simple most people will understand it. Even if they couldn’t they will be able to point to someone nearby who can understand. In addition to English, there are professional drivers, guides and major hotels who can communicate in a variety of languages such as German, French, Italian, Hindi, Arabic, Japanese and Chinese. If you do not speak English it is advisable to pre-arrange drivers and guides who can speak your language.
When traveling to a foreign country some travelers like to learn some phrases of the language of their destination or make use of a phrasebook. While this is great, I highly doubt speaking few Sinhalese phrases will be of much use in Sri Lanka because most people understand basic English phrases and none of the locals expect tourists to speak local languages. So it is advisable to use simple English anywhere you need to communicate and it is totally acceptable to use basic English phrases such as Good Morning, Thank You or Bye with any local even if they don’t speak English because almost everyone understands those basic terms.