I covered this in considerable detail here, and hopefully this will answer most of your questions.

The tl;dr is that the Crimean Khanate organised regular slaving raids into the borderlands of Muscovy and the Polish-Lithuanian Commonwealth, as well as acting as an entrepot for slaves brought from other areas adjacent to the Black Sea, such as Circassia. About a third of the slaves remained in the khanate and the remainder were sold on, often ending up in the slave markets of Istanbul.

The Khanate's trade was, incidentally, only a successor to a similar one organised by the Genoese and Venetians when they were in control of the Crimea prior to the fall of Constantinople in 1453 – something that's important to make clear, as the trade is nowadays often fastened on to by white nationalists who try to use it to argue the point that "whites have been enslaved by blacks".

The trade as a whole lasted for at least six or seven centuries and was only ended by the southern expansion of the Russian empire in the eighteenth century.