How was the slave trade organized and who controlled each aspect of the trade?
The Atlantic slave trade was taking place between Africa and the Americas, for the most part. Of course, different people participated in it at different times and different people profited from it.
In general, the slave ships tended to be English. They could be from England or they could be from the Northern colonies of North America (Massachusetts, etc). These traders profited a great deal from taking the slaves to the Americas and from shipping American goods such as rum to England. Profits were also made by people who outfitted the ships and the people who wrote insurance policies for them. In other words, many people in the North profited.
It is also worth noting that some Africans profited. Specifically, the Africans who caught other Africans and sold them to the slave traders made a great deal of profit from their part in the trade.