The languages that slaves spoke were varied; there was no single language that they all spoke. Some examples include the Yaruba, Igbo, and Hausa languages, all of which were from tribes in present day Nigeria, which happened to be where most slaves going to the 13 colonies and the West Indies came from. Over time, these languages tended to merge together (with English), and in one particular case a unique language evolved in South Carolina called Gullah. Some examples of African words that have emerged into the modern American-English dialect include goober, voodoo, and gumbo.

Source: Kennedy, David M., and Lizabeth Cohen. The American Pageant: A History of the American People. Boston, MA: Wadsworth Cengage Learning, 2014. Print.

Every slave importing country/colony in the new world had differing manners of "integrating" slaves into their system. In the US it was common practice for slave owners to outlaw native languages and religion. There are various reasons for this but the main two being that it was believed that they would be more easily controlled and produce children (more slaves), and the fear of revolt (native languages cold be used for slaves to organize themselves).

In Brazil, for example this was not the case because they were so much closer to Africa that the slaves were substantially cheaper. Their system was based on working a slave, to death often times, and importing a new one. They didn't bother with assimilation. Because of that, today African Brazilian culture has many more similarities to West African cultures.

Source: sorry no books on hand. I was an African Diaspora major and wrote my senior thesis on Jamaican slave revolts.