Much of my answer will be based on my knowledge of English slaving, with only supplemental information for Portuguese/Brazilian, French, Danish and Dutch trading.

The simple answer is that there were established ports and cities on the African coast where European slave ships would arrive to purchase cargo. There were eight European trading regions along the African coast, but these were European constructs. Within the regions there was significant variation over who had a right to trade, what African ‘nation’ controlled the territory, and what commodities could be sold. Here is a useful map showing the various regions. These are the English names for the regions, though some of these varied over time:

Senegambia
Sierra Leone
Windward Coast
Gold Coast
Bight of Benin
Biaght of Biafra
West Central Africa/Angola
Southeastern Africa & Madagascar

The trade in each region varied over time, though there were some consistencies. Portugal and Brazil, due to their influence in Anglola/West Central Africa purchased most of the slaves embarking in that region. The English traded in every region, but the majority of slaves were purchased along the Gold Coast and in the Bight of Biafra. France traded mostly in West Central Africa and the Bight of Benin. Overall West Central Africa was the largest exporter of slaves, selling about 5.7 million slaves to European trades. The three next largest trading regions were the Bight of Benin (2 million), the Bight of Biafra (1.6 million) and the Gold Coast (1.2 million).

In order to purchase slaves, the slave ships from Europe would sail down to the coast to a region either the slave ship owner, or the slave ship captain was familiar with. The correspondence showing how these decisions were made can be rather sparse, but there are a few collections worth noting. Robin Law has edited a 3 volume work of letters from agents of the Royal African Company on the “Slave Coast’ (Bight of Benin) from 1681-1700. They sent regular dispatches to London to inform them of the latest political news, what trade goods were in demand, and any interference or illegal trading done by other Englishmen or other Europeans. While some items, like tobacco or guns, were always in demand, the various textiles that made up a major part of all the trades could fall in and out of fashion quicker than Englishmen could react. Africans could and would be very particular about the patterns, fabrics, colors, etc. of the material they purchased. (See Alpern, “What Africans Got For Their Slaves; A Master List of European Trade Goods” History in Africa (1995)).

Slave ships would stop in at various points along the African coast to trade. Very rarely was a slave ship ever filled at the first stop. The Diligent, a French slave ship in 1731-1732 spent nearly 8 weeks along the African coast, trading at different stops and towns. The cities themselves were not large by European standards (at least in the eighteenth century). Elmina, one of the primary slave trading locations on the Gold Coast had approximately 15,000 people in the later part of the eighteenth century. Ouidah, the principle slave port in the Bight of Benin had less than 10,000 people (Law, Ouidah).

The procedure for trading in towns varied by location, so I will give just a general outline of what happened. Most slave ships stayed off the coast, partly because the shores were too shallow for normal ports, partly to prevent the spread of disease, and largely to prevent/deter slaves already on board from escaping. Part of the crew, the captain, and possible the ship’s doctor (or chirurgeon), who would help check the health of slaves, rowed to shore to conduct trade. Typically, a gift (or payment for the privilege) was made to the local head of state (typically called chieftens or kings by Europeans, but this would not have been a title the Africans recognized) in order to allow the men to start trading. Slaves were kept in holding cells called barracoons, or in the various holding places available. Elmina was a slave trading castle built on the Gold Coast by the Portuguese. Some of the enslaved Africans at Elmina were kept in dungeons, but this was more an exception than the rule.

Slaves could be bought piecemeal or in groups, mostly depending on how the African slave trader wanted to operate. The slave trader thought in economic terms about the people he sold; low supply, higher prices, glut in the market, sell by bulk. It cannot be overstated how much power the African side of the trade wielded over the European. The image that Roots gave us of a captured slave taken by white and African men is a myth. For the most part, Africans were brought to the coast from the interior as a result of wars, criminal proceedings or general sale. The slave captain negotiated with the local slave dealers, trying to maximize the number of young men in his slave cargo. For the Africans, young men were the least desirable to keep (young women being the most valuable), so both sides felt they got the winning end of this deal. Some slave traders would shave and rub palm oil on older men to make them appear younger – this lead to the very odd image of slave captains licking the faces of Africans to see if there was beard stubble on their faces. Certainly, this helped convince some Africans that they were being sold to be eaten.

After trading along the coast for a few weeks to a few months, the slave captain would depart for the Caribbean or Brazil with a cargo hold full of slaves. While the “Middle Passage” is the most infamous part of the slave trade, it was not the most deadly. The travel from the interior of Africa to the hull of a slave ship likely had a 50% mortality rate, compared to the 10-20% in the Middle Passage. Besides the number of Africans that would die in slave raids or open warfare, the slave holds and barracoons spread disease among an often starved population. African slave traders and the rulers displayed their wealth and power, which was often commented on by the European visitors. While the slave ‘ports’ may not have been cities the size of Bristol or Liverpool, they still were the centers of international trade on the African coast. By and large, they were ruled by Africans with an iron fist, and any European who lived on the coast did so with the permission of the ruler.

One last note – much of the above is true for the area from Senegambia to the Bight of Biafra. I have not reread Miller’s Way of Death for West Central Africa in a few years, and the Portuguese system of government and trade may have been quite different from the way the French, Danish and English traded farther north and east.