Some of this depends on what specific time and region you're discussing, but the short answer is, "a lot." There's been a historical tendency to downplay the sophistication of Native American polities because they weren't organized as (nor intended to reflect) European nation-states. However, native polities as they did exist were often flexible and expansive, incorporating groups with diverse opinions and diverse roles, while seeking a governance model typically based more on consensus than coercion. The result of this governing model were often leaders with a keen grasp of negotiation, compromise, and an attention to nuance and detail. Thus, they paid close attention to the different groups of Europeans that arrived and quickly distinguished between the different behaviors and beliefs of the different groups. Furthermore, Europeans frequently told the natives who they were and who their enemies were. And, on top of that, sixteenth and seventeenth century expeditions routinely kidnapped young Native Americans to educate in Europe as future translators and, hopefully, ambassadors of European customs and religion.

To provide two rather simple examples, we can look at the reactions of Powhatan in Virginia and Massasoit in Plymouth Colony. Powhatan grew up seeing Spanish ships cruise along the coastline, perhaps occasionally venturing into the mouth of the James River. His cousin, Paquiquineo, was kidnapped by the Spanish and educated in Spain, being renamed Don Luis de Velasco. In 1570, Don Luis returned with 2 Jesuit missionaries to his home and, after they attempted to form a mission, had them and all but one boy with them slaughtered. The English who arrived in the area in 1607 were given a similarly hostile reception. Their only saving grace was their number and armament. However, Powhatan recognized the difference between the English and the Spanish and so did his rivals, the Chickahominy, who hated the Spanish but traded willingly with the English. Powhatan made sure to question John Smith about his home and its rivals and culture when Smith was his captive. Powhatan used the presence of the English and his "adoption" of John Smith, a known leader of the English, to solidify his already impressive control over his coalition and hopefully gain English support against enemies like the Iroquois.

Massasoit of the Wampanoag represents a similar story with some key differences. The native polities in the future New England region had extensive contact with fishing and trading parties from Europe (contact that was both profitable and violent), but less contact with colonizers. One exception was Tisquantum (known to most schoolchildren today as Squanto), another example of a young Indian kidnapped and turned into a translator. There was less European imperial rivalry in New England in 1620. France had established Quebec in 1608, but their contact was largely limited to the Montagnais, Alquonkin, and Huron until much later. Instead, Massasoit, who knew of the weaponry and trade potential of the English, saw the Pilgrim settlers of Plymouth as an opportunity to improve his position in intertribal conflicts. Disease had wiped out much of his population and severely disrupted native territorial claims and political alliances in the region (Tisquantum, who had hoped to lead his village upon his return, instead discovered he was the last one of his village who was alive). The first significant military action taken by the Pilgrims was at the behest of Massasoit against his enemies, the Massachuset.

If we move further into the seventeenth and eighteenth centuries, we see Native American polities playing key roles in how the European colonies formed, expanded, and warred. Most notably, were the Iroquois Confederacy, who, while allied with the Dutch and then the English in New York, reached their own peace with the French, and used their influence with the English to bring tribes like the Delaware and the Lenape under the umbrella of their control. For much of the eighteenth century, you could plausibly argue that 3 great empires existed in North America: the French, the British, and the Iroquois. Richard White discusses the give-and-take in the "pays d'en haut," (today's Great Lakes region of the US) between Algonquin-speaking peoples and the French and British as one of constant negotiations over power and political legitimacy that last for two centuries before the expansion of the United States throws off that balance. Native peoples could only accomplish this in the face of severe manpower shortages due to disease if they intimately understood how to play the French and the English off one another while also negotiating with neighboring tribes that had different relations with the imperial powers.

If you're looking for reading suggestions, I recommend Colin Calloway, New Worlds for All: Indians, Europeans, and the Remaking of Early America, James Axtell, Natives and Newcomers: the Cultural Origins of North America, Camilla Townsend, Pocahontas and the Powhatan Dilemma, Richard White, The Middle Ground: Indians, Empires, and Republics in the Great Lakes Region, 1650–1815, and for something more focused on the late eighteenth and early nineteenth centuries, check out Gregory Evans Dowd, A Spirited Resistance: The North American Indian Struggle for Unity, 1745-1815.