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.
The bulk of the Atlantic slave traders kidnapped Africans from the west coast of the continent, often referred to as the "Slave Coast", and started with the Portuguese and Spanish in the 1500's, then spread to the Dutch, British and to a lesser degree, Americans.
Many of these slaves were taken to Brazil (3 million +), and the Caribbean to posts like Barbados where they were sold to other cash crop plantation owners in other colonies, or in the United States. Many slaves ended up in Cuba and Haiti, while a relatively small percentage of slaves from this trade were brought to the present day US.