how were the slavers known to travel in order to capture people?

I'm not a historian on this matter, but I can answer this.

The people who were capturing the would-be slaves were not Europeans. They were other Africans.

There already were slaves in West Africa even before European influence, but it was pretty different from, say, slavery in 18th-century Haiti; for example, many slaves in Africa actually did very little, and were there to show the wealth and power of the owner. Much slave labor was "occasional work performed as a tax or tribute," and slaves were more likely to be eventually freed. Traditional African slavery had some brutal aspects as /u/JMBourguet notes below, but it was generally less brutal than chattel slavery in the Americas. The slaves could be criminals, voluntary slaves, but especially, war captives.

When the Europeans arrived, the slave "production" increased. Slaves included "scofflaws, tax cheats, political exiles, [and] unwanted immigrants," and sometimes kings and leaders hiked criminal penalties to have more criminals and thus have more slaves to sell. But in general, most slaves came from war: war captives, from raids or battles. Sometimes an important person in the enemy polity was abducted and a ransom of, of course, slaves was demanded.

The Africans got weapons, manufactured goods, and other valuable things in exchange. African demand was as important as European demand; for example, Asante traders brought slaves to a Dutch fort in 1732 and demanded that the Dutch buy the slaves and sell their flintlock guns in exchange (flintlocks were superior to matchlock guns). The Dutch governor felt threatened, and had to order all flintlocks to be sent to the fort at once. The rise of Dutch export in slaves in the 1720s may be directly linked to Asante selling slaves and buying arms to have a competitive edge against its neighbors. This was not limited to Asante; for example, the King of Dahomey also obtained much of his wealth from the slave trade.

Hope I helped a bit. My source:

1493: Uncovering the New World Columbus Created, by Charles C. Mann

There weren't mass migrations from the coast, primarily because the city-states(Calabar, Opobo etc) and Empires on the Coast(Asante and Dahomey) were the primary suppliers of slaves. In fact in the case of Dahomey and Asante their primary motivation for the conquest of the former coastal dwellers was to gain access to the Trans-Atlantic trade. However in the interior, a vicious cycle was going on(N.B I can only speak for the Nigerian interior here) the Oyo empire collapsed during this period, as such an important regulator in the trade was lost. This led to a Sengoku jidai like period in the West of present day Nigeria, where military city states engaged in constant warfare first to stop the Sokoto Jihadists and eventually among themselves. The losers were of-course sold into slavery. When the Caliphate's march to the sea was halted, the powerful city states at the time were Ibadan, Ijebu and Ijaye, in order to achieve superiority, they needed guns and to get guns they needed slaves so they conquered smaller cities, the survivors of the smaller cities then banded together and raided even smaller cities for slaves because slaves meant guns and guns meant power. Eventually the abolitionists had their way, trade switched to primarily palm oil and slaves were needed for Palm plantations. In-fact a common excuse used for the conquest of Nigerian territories was to put a stop to the slave trade. So summary, they weren't mass migrations because migrations meant going either towards the slavers of Asante or Dahomey or North towards the caliphate who were also slavers, given that choice most chose to fight leading to the development of merit based military societies, well except for the Igbos whose rain forests and hilly regions kept them isolated.