Final answer:
European citizens moved to the Americas by a combination of riding on ships, paying for passage, and having documentation, which varied in form but served as an early type of passport. The broader context includes trade, piracy, colonization, cultural impact, and forced immigration.
Step-by-step explanation:
How European citizens decided to move to the Americas depended on several factors and cannot be succinctly answered by any single choice provided. Historically, this process involved a combination of a) riding ships across the Atlantic, b) traditionally paying for a seat on the ship, and to a lesser extent, c) having some form of documentation which could be considered an early form of passports. While formal passports as we understand them today were not in use at the height of early European emigration to the Americas, some form of identification or permission to travel and settle was often required by governing authorities of the time.
The subject of moving to the Americas is broad and encompasses elements of legitimate trade, piracy, and smuggling as practiced by powers like the Dutch in the Caribbean, as well as broader social and economic factors such as the search for new routes to Asia, the establishment of settlements and colonies, changes in agriculture, and the displacement and subjugation of indigenous peoples and African slaves.