It varied a great deal. In some times and places early corporations held a strangle hold on the market. In others there were more independent ventures. A group of merchants could get together, finance a voyage, and when the ship returned split the profits like they did for any other cargo.

If you are interested in getting and inside look at the trade there is an excellent book that came out not long ago. The Diligent : a voyage through the worlds of the slave trade by Robert Harms is a discussion of the voyage of the titular vessel which bases its core around the diary of one of the ships minor officers. It starts slow, but if you can power through the first 60 pages of background Harms gets to when the ship leaves France for its voyage and it picks up. It is an incredibly detailed look at the process from start to finish as an independent trader.

Harms structures the book much like a travel log. He presents First Lieutenant Robert Durands comments if any and then fleshes out more details on each of the places visited. Most pertinent to your question I think is the first few chapters which discuss how the French companies lost their crown monopoly which allowed independent traders like the Diligent to thrive.