The official language of the Dominican Republic is Spanish. You will find some Spanish-English bilingual locals especially in Santo Domingo and tourist areas. Many Dominicans have spent considerable time in the United States, especially New York City, and enjoy speaking English with foreigners in order to keep their language skills sharp. If you speak some Spanish, most Dominicans will try hard to meet you half way and communicate.
If you have a problem, you can probably find someone who speaks sufficient English (or probably French and possibly German or Italian in tourist areas) to help you out. Dominicans are quite friendly and will be quite helpful if you are polite and respectful. The large community of Haitians living in the DR speak Haitian Creole and in some cases French, and most speak Spanish well. In rural areas, you may hear a few African and Arawakan words interspersed with the Spanish, but standard Spanish is universally understood. Communication should not be a problem even for those who speak only a minimum of Spanish. If you are traveling to one of the large all-inclusive hotels, you will have no language problems.