I can't imagine they just sailed to Africa, waited in some bushes with giant butterfly nets, then jumped out whenever someone passed by.
This part was always left out of the history books. I don't understand why. It seems like one of the more important aspects and to just be forgotten makes no sense to me.
Actually, you're not far off with the butterfly net hypothesis. Here's how it usually went in broad terms:
European traders showed up with manufactured goods that Africans wanted/needed. In exchange, the Europeans wanted slaves.
Because there was an economic incentive to do so, various tribes/groups of Africans maintained a constant state of war with their neighbors as a pretext for launching slave raids.
Captives were sold to the Europeans, who transported the new slaves to plantations in the Caribbean, etc.
Those slaves raised crops of various sorts, but often sugar or molasses. Sugar and molasses were made into rum.
Profit from the rum was used to buy manufactured goods.
Go to step 1)
What I've just described is known as the Triangle Trade. Slaves->Rum->Manufactured Goods.
So that's half the equation. The other, obvious component, was that slaves had children. They were encouraged to. Those children--even children fathered by the slave's white owner--were also slaves.