The official language of Cuba is Spanish, quite similar to the Dominican Republic and Puerto Rican Spanish, although the version here is quite different from that spoken in Spain (although quite similar to the one in Canary Islands because many Cubans are descendants of Canarians), Mexico and South America. Cubans tend to swallow the last syllable in a word and generally swallow the 's' sound.
Basic to fair English is spoken in some tourist locations and language should not be a deterrent to visiting the country for non-Spanish speaking tourists capable of speaking English, though basic Spanish would prove useful, especially in more informal settings. Cubans enjoy talking to tourists, especially if you are staying with them in the "Casas particulares" and some knowledge of Spanish will help you understand regular Cubans' experiences.
Instead of the Spanish "Que tal?" for "How are you?", Cubans will say "Que vola?" (similar to "What's up?", generally quite informal) or "Como andas?" (literally means, "How are you walking?"). Young Cubans amongst themselves will use the word "asere" which means "buddy" but is generally used between men and is not recommended for use by women.