They asked the people who lived there, or interacted with the people, at the very least. Tales of Native Americans supplying early colonists to the British North American colonies with food, or even teaching them how to grow indigenous crops, is part of the foundational mythology of the United States. Sharing food between people, however, often just shows up as something people do when they meet and start interacting with other peoples. After all, everyone needs to eat.

For instance, Bernal Díaz del Castillo, in his True History of the Conquest of New Spain, states that the Spanish crew exchanged bacon for native goods, and likewise he gives multiple accounts of the Spanish trading their goods for fowl, "maize-bread," and various (often unnamed) fruits and vegetables. In this case, explorers arriving in the Americas were able to determine what plants and animals were safe to eat because the people who have been living there for thousands of years, and had in some cases domesticated the foods, were making quite obvious what was food. This even extended beyond staple goods to more exotic fare, such as the dishes consumed by Motecuhzoma, which involved so many foodstuffs that Díaz del Castillo says that "it would have been no easy task to call them all over by name." My favorite tidbit though, is his take on the spirulina algae harvested from the lakes and pressed into cakes, which Díaz del Castillo described as having " a similar taste to our cheese."

We also see more encyclopedic approaches, such as with the pages upon pages Sahagún devotes the foodstuffs available in the markets of Tenochtitlan-Tlatelolco, including listing of various types of beans, an astounding array of tamales, several styles of chocolate drinks, and turkeys of different levels of quality. Cortés likewise rhapsodizes about the bounty of the market place, often showing how the Spanish were interpreting this New World through their own schema, referring to various American fruits and vegetables as being like a Eurasian equivalent. So we have him referring to artichokes, cherries, and watercress, all native to Eurasia, and interpreting maguey sap as honey and pulque as wine, leading him to write, "honey is also extracted from the plant called maguey, which is superior to sweet or new wine ; from the same plant they extract sugar and wine, which they also sell."

Cortés' descriptions pale in comparison to later, more academic and rigorous chroniclers. The aforementioned Sahagún, for instance, spends almost an entire book of his General History of the Things of New Spain listing various plants and animals, giving a brief description and then often noting their culinary or medicinal uses. The plant tlilxochitl, for instance, is described thusly:

It is cord-like, like cords, slender. Its vine is like the tetzitzilin; it is a climber, one which sends out shoots. It has a bean. Its bean is green; when dry it is black. It is glistening; within, it is resinous. It is of pleasing odor, fragrant -- a precious thing, wonderful, marvelous. It is of pleasing odor, perfect, superb. It is potable in chocolate. it creeps, constantly creeps, travels, sends out a shoot, forms foliage, produces a bean, forms a bean.

The exotic vegetation being described is, you may have guessed, vanilla. The above passage may actually be the first description of vanilla by Europeans, and, in noting the spice's potability in chocolate, Sahagún presaged its dominant use by Europeans for centuries: as a chocolate additive. (For more on the introduction and evolution of chocolate in Europe, I highly recommend Sophie and Michael Coe's The True History of Chocolate.)

An exploration of the less culinary and more medicinal side of plants and animals was conducted by Francisco Hernández, the royal physician to the Spanish King Phillip II. He spent the better part of the 1570s travelling throughout Mexico and cataloging plants in use by the indigenous population. Like Sahagún, or perhaps even more so, his primary source of knowledge for the use of these plants were the native people themselves, though he seemed to never miss a chance to disparage his local informants lack of adherence to the Galenic humoral system.

Food, more so than medicinal, chauvinism, was the more common complaint by Europeans in America. The primitive state of medicine at the time, combined with its practice being the province of elites, may have led to a sort of ecumenicism. Hernández, for instance, presents the medicinal uses of innumerable Mesoamerican herbs without comment more often than he scoffs that some plant which is obvious "cold" is being used as though it were "hot." The Codex Badianus, a mid-15th century text, spices predominantly Mesoamerican remedies with the occasional Western European ingredient without comment. Yet while the physicians on either side of the Atlantic might be happy to adopt and adapt, colonial stomachs often yearned for home. Earle (2014) in The Body of the Conquistador: Food, Race and the Colonial Experience in Spanish America, 1492-1700, for instance, notes that early colonists were advised to pack their own foods "because neither wheat bread nor wine is to be found in those parts," and likewise relates that Jeronimo Aguilar, a long shipwrecked Spaniard who acted as Cortés' first translator, felt the need to slowly re-introduce foods into his diet, as he found his stomach had adapted to the Mesoamerican diet and "would regard Christian food as foreign."

Early European travelers to the Americas, or at least to Mesoamerica, were greeted by a populous country overflowing with new plants and animals, but also a people who had no inclination (and why would they?) to hide their own diet. They were not arriving in an empty land, but rather one which had been shaped by millennia of human work, including the domestication of plants and animals. Europeans learned what plants and animals were food, medicine, and/or poison from the people who had lived and cultivated those products for generations.

There's a whole side tangent about exploitation of African knowledge for early cash crops like rice and indigo that I kind of want to go into, but it's far afield from everything above, so I'll just point you towards Carney (2001) Black Rice as a good introduction to the way early Southern planters relied upon the long established expertise of Africans.

And there's another tangent about how the influx of American products and knowledge influenced European science and may have been a major spark for the Enlightenment (the influx of capital no doubt helped). I touch on this more explicitly in a past comment.