How did America become a British colony?

Britain made its claim to America during the Age of Discovery. After the fall of Constantinople to the Ottomans in 1453, Europeans began to explore distant lands in search of a route to the riches of Asia. The first nations to launch expeditions were Spain and Portugal. Britain and France followed their example some years later. Holland also became engaged in exploration, but its only colony in North America was later conquered by Britain.
In 1497, five years after Christopher Columbus's famous voyage, John Cabot claimed North America for Britain. Cabot was a Venetian who sailed for Britain. Spain became heavily involved in what became Latin America and did not move north of Florida. Spain's acquisition of wealth in the "New World" inspired other European nations to try to emulate it.
Britain established its first colony in 1585 at Roanoke in modern-day North Carolina. For unknown reasons, this colony was abandoned a couple of years later. Britain's first permanent colony was set up at Jamestown in 1607.
Britain had powerful enemies during the Age of Discovery. Spain had been the dominant power, but Britain defeated Spain in 1588. France later emerged as a strong rival to Britain in North America, but Britain defeated France in a series of wars in the eighteenth century. These military victories meant that Britain became dominant in North America.