Most African slaves were captured by other Africans and then sold to European slave traders on the African coast. These slaves came from a number of sources. Enemy soldiers and civilians, debtors, and occasionally even kidnapped people. The African slavers sold them to Europeans for a variety of valuable goods. The thing is, that most slaves in Africa had a very different status from slaves in the western hemisphere. In Africa, most slaves were not chattel, but had certain rights and could even hold state offices. However, once they were sold to Europeans, slaves found themselves as chattel with precious few rights, if any at all.

For more detail about the slave trade in Africa check out Sylviane Diouf, Fighting the Slave Trade.

This answer is a little more complicated.

Many slaves were brought into the Americas not from Africa but from the Caribbean. These slaves worked in sugar cane plantations, spoke some English, French, Spanish possibly, and their skin was lighter. Slaves from the Caribbean were used all over the colonies. The majority of slaves direct from Africa were in the South, but the majority of slaves in the US (as a whole) came to the US via the Caribbean. This article was a very interesting read, and has a lot more detail.