Answer: It began with Portuguese merchants buying slaves from the king of Benin.
Explanation: African slaves prior to 1441 were predominately Berbers and Arabs from the North African Barbary coast, known as ‘Moors” to the Iberian. They were typically enslaved during wars and conquests between Christian and Islamic kingdoms. The first expeditions of Sub-Saharan Africa were sent out by Prince Infante D. Henrique, known commonly today as Henry the Navigator, with the intent to probe how far the kingdoms of the Moors and their power reached. The expeditions sent by Henry came back with African slaves as a way to compensate for the expenses of their voyages. The enslavement of Africans was seen as a military campaign because the people that the Portuguese encountered were identified as Moorish and thus associated with Islam. The royal chronicler Gomes Eanes de Zurara was never decided on the “Moorishness” of the slaves brought back from Africa, due to a seeming lack of contact with Islam. Slavery in Portugal and the number of slaves expanded after the Portuguese began exploration of Sub-Saharan Africa.
Extra explanation: Explanation above is official recognized but there are a lot of evidence that slave trade started even 2nd century BC by the Roman Portugal and it proceded to: Visigothic and Suebi kingdoms, Islamic Iberia, and Reconquista. But she certainly didn't start with Portuguese merchants buying slaves from the king of Benin.