Two ways which were both well documented in the early accounts of English settlers.

First, the English learned the language from the native Americans simply by interacting. By the time John Smith took his first voyage around the Chesapeake Bay in 1608 he could speak Algonquian well enough to communicate with the locals on the Eastern Shore of Virginia. When he ran into two Indian men in a canoe fishing at Cape Charles on June 3, 1608 he spoke their language well enough to be directed by the fishermen to the village (Accomack) where the chief lived, near present day Old Plantation Creek. The chief told him that all of the harbors to the north were good for canoes, but not deep enough for ships. Their communication evidently had a relative level of sophistication. This is 13 months after Smith first landed at Jamestown. He had spent time the previous winter as a captive of the Indians and evidently learned some of the language during that period.

Also, several English boys -- notably Thomas Savage and Henry Spellman -- were sent to live with the Indians with the express goal of learning the language and serving as interpreters. Savage was sent to the Eastern Shore and became such a favorite of the Indian King of the Eastern Shore of Virginia that the King gave him several thousand acres of land on the Chesapeake Bay which is today called Savage Neck (in this part of the world, a neck being a peninsula with relatively narrow tidal bays called creeks on each side). Spellman and more particularly Savage were utilized frequently as interpreters in various official contexts throughout this early period.

It is also possible that some Indians the settlers would have encountered knew some English or other European languages. Rountree et al. (2007) indicate that English from the Roanoke Colony stayed several month with a Chesapeake tribe in 1585-6 and that English and other European ships probably visited the Eastern Shore of Virginia prior to 1607. To be clear, I cannot find any contemporaneous references to the Indians knowing English words in the Chesapeake when first contacted by the Jamestown settlers.