I'm most familiar with Aztec food, so I'll talk on that.
The most common foodstuff in the Aztec Empire was maize, or corn, which was often made into tortillas (usually rolled around food like tacos or dipped into it), tamales, an early form of pozole soup, or atole (a simple gruel). Corn was literally worshiped to such an extent that women would blow on it before putting it in the fire and believed they would be cursed with famine if they threw away corn that fell on the ground instead of picking it up. The Aztecs would nixtamalize the corn, treating it with limewater; this improved the taste and made it easier to grind, but it also had the unknown benefit of releasing nutrients that normally wouldn't be absorbed by the body. This would create a problem for later Europeans and North Americans who consumed a corn-heavy diet without knowing to nixtamalize it and suffered nutrient deficiency disease.
Corn was consumed in some form at virtually every meal. The simplest Aztec meal was a few tortillas with a dipping sauce made from chili peppers, water, and optionally tomatoes, maybe served with some beans. However, there was a massive amount of ingredients available in various combinations. They grew amaranth and chia, spirulina algae was gathered from the lakes and dried, fruits and vegetables like prickly pear and chili peppers harvested, and animals were hunted and fish caught. Meat was relatively uncommon because the Aztecs never engaged in widespread animal husbandry to the scale the Old World did, so there was also a lot more consumption of insects. And yes, they did eat human sacrifices.
Obviously, we all know about the Aztecs and chocolate. Chocolate is naturally very bitter and didn't achieve its modern sweet form until Europeans started adding as much sugar as they could, so chocolate was typically consumed as a room temperature or warm drink flavored with chili and honey and thickened with ground corn.
Cooking was generally done with a pot that the Spanish called the olla. You would simply fill it with water and either boil the food or steam it on a layer of twigs over the water. Many herbs and spices were available, with the most common being hot peppers, but the only sweetener really available was honey.
For drinks, the traditional alcoholic drink was octli, known in Spanish as pulque. This is an odd-tasting sour drink made by fermenting agave sap. They also made a form of mead called balché by soaking the bark of the balché tree in honey and fermenting it in water, as well as prickly pear wine.
Despite this, modern Mexican cuisine is a fusion with Spanish cuisine and owes just as much to Europe as it does the natives. The Spanish brought animal husbandry of cows, pigs, goats, chicken, and sheep. They brought dairy (something virtually unknown in Central America and many parts of Asia before being brought through imperialism), wheat, barley, rice, and alcohol made from these grains. They brought oil from seeds and olives and the use of lard for frying, something many Native Americans initially found utterly disgusting. And they also suppressed many native foods and beverages like pulque to remove as much native culture as possible.
Take your typical street taco, for instance. You've got beef or pork with cilantro, onion, and lime juice seasoned with hot sauce, garlic, and cumin on a tortilla. Out of all the ingredients, only the chili peppers in the hot sauce and tortilla are native Mexican products, and the tortilla doesn't even count if it's made with wheat flour!