If you're visiting the Caribbean and you speak English, you're in luck: English is the first- or second-most spoken language in most Caribbean destinations and is the unofficial "language of tourism," as well. However, you'll often find that your travels will be more richly rewarding if you can speak with the locals in their native language. In the Caribbean, that's usually determined by which colonial power—England, France, Spain, or Holland—held sway over the island first or longest.
The British first established a presence in the Caribbean in the late 16th century, and by 1612 had colonized Bermuda. Eventually, the British West Indies would grow to become the largest group of islands under one flag. In the 20th century, many of these former colonies would gain their independence, while a few would remain British territories. English would remain the dominant language in Anguilla, Bahamas, Bermuda, Cayman Islands, British Virgin Islands, Antigua and Barbuda, Dominica, Barbados, Grenada, Trinidad and Tobago, Jamaica, St. Kitts and Nevis, St. Vincent and the Grenadines, Montserrat, St. Lucia, and Turks and Caicos.
Funded by the King of Spain, Italian navigator Christopher Columbus famously/infamously "discovered" the New World in 1492, when he landed on the shores of the Caribbean island of Hispaniola, in the present-day Dominican Republic. Several of the islands subsequently conquered by Spain, including Puerto Rico and Cuba, remain Spanish-speaking, although not Jamaica and Trinidad, which were later seized by the English. Spanish-language countries in the Caribbean include Cuba, Dominican Republic, Mexico, Puerto Rico, and Central America.
The first French colony in the Caribbean was Martinique, established in 1635, and along with Guadeloupe, it remains a "department," or state, of France to this day. the French West Indies includes French-speaking Guadeloupe, Martinique, St. Barts, and St. Martin; French also is spoken in Haiti, the former French colony of Saint-Domingue. Interestingly, you'll find a French-derived creole (more on that below) spoken on Dominica and St. Lucia, even though the official language is English on both islands: as was often the case, these islands changed hands many times during the war for the Caribbean between the English, French, Spanish, Dutch, and others.
You still may hear a smattering of Dutch spoken on the islands of St. Maarten, Aruba, Curacao, Bonaire, Saba, and St. Eustatius, which were settled by the Netherlands and still maintain close ties to the Kingdom of the Netherlands. However, English is widely spoken in these islands today, along with Spanish (owing to the close proximity of Aruba, Bonaire, and Curacao with the coast of Spanish-speaking Venezuela).
In addition, nearly every Caribbean island has its own local patois or creole that locals use primarily to speak to one another. In the Dutch Caribbean, for example, this language is called Papiamento. It's not uncommon to have island residents speak to each other in rapid-fire patois that can be unintelligible to unfamiliar ears, then turn around and address visitors in perfect schoolhouse English!
Creole languages vary greatly from island to island: some, incorporate French terms with bits of African or native Taino language; others have English, Dutch, or French elements, depending on who happened to conquer which island. In the Caribbean, the Jamaican and Haitian creole languages are considered to be distinct from the Antillean Creole, which is more-or-less standard across St. Lucia, Martinique, Dominica, Guadeloupe, St. Martin, St. Barts, Trinidad & Tobago, Belize, and French Guyana. In Guadeloupe and Trinidad, you also will hear terms derived from South Asian tongues—Indian, Chinese, Tamil, and even Lebanese—thanks to immigrants from these nations who also have made their presence known in the form of language.