The slave trade as a powerful historic phenomenon obviously had its own historical premises and peculiarities. There were certain mechanisms through which the slaves were sold and bought, and all of them are mostly connected with the needs of the time when the new lands were discovered.
In fact, slavery existed long before the Western Hemisphere was discovered, but the age of geographical and technical advance brought new rules into the game. The slaves transferred from the Eastern hemisphere to the South and North America were generally brought from Africa. There were several ways the Africans became the American slaves.
Firstly, they were purchased by the Europeans (the Portuguese, the Dutch, and the English etc.) from the local African kings or tribal leaders. These were usually the captives from the neighboring or rival tribes. Sometimes the leaders sold the criminals in order to prevent their society from their recidivism.
Later the slaves also became the part of the economic cycle known as the triangular trade. First the goods were sold to the African population from the Europeans (guns, ammunition and so on); then, the slaves were taken from Africa and transferred to the American across the Atlantic ocean; finally, the goods were brought back from the new lands to Europe. These were goods produced by the efforts of the African slaves.
Apart from that, the Europeans to a great extent enslaved free population as well. They seized them during raids performed at the shores of Africa. The merchants were later awarded with the license for trading the enslaved people to the colonies of the Spanish empire. It was economically motivated, as the vast lands in America required much labor for a lot of kinds of work, including works at plantations, in mines and in household. In this way, the slave trade process was tightly connected with the process of colonizing the Western Hemisphere.
Klein, Herbert S. and Jacob Klein. The Atlantic Slave Trade. Cambridge: Cambridge University Press, 1999.
Solow, Barbara (ed.). Slavery and the Rise of the Atlantic System. Cambridge, Cambridge University Press, 1991.