In Handbook to Life in the Aztec World, Manuel Aguilar-Moreno writes that
The common Aztec ate only two or three tortillas and a serving of beans at each meal.
We appear to have a great deal of evidence about how the tortillas were made, but do we have clues about how the beans might have been prepared?
Aguilar-Moreno also writes that other foods, including squash and avocado, could supplement an Aztec commoner's diet. Do we have any clues about how those were prepared? As for the Mayans, etc, do we have any information on their methods of preparation for similar foods?
Beans would, of course, be boiled. Typically this would be done fresh or dried chilies to form what Coe, in America's First Cuisines, calls a sort of "stock" which could used for any number of other dishes. To this basic preparation, any number of other ingredients could be added. A common addition was epazote or some other green, but (re)adding chilies was of course to be expected. The "stew" of beans could be thickened with tortillas or maize dough. Regardless, the dish would be scooped up with tortillas.
Squash, roasted or boiled (the two staple preparations of Mesoamerica) could also be added to the beans. Squash was not just used for its flesh though, with its blossoms being added to atolli and ground squash seeds used in any number of applications. Aside from also being used as a thickener, Coe also mentions a preparation of dried and reconstituted beans-in-pod being served with iguaxte, which is a squash seed and tomato sauce. SahagĂșn also specifically mentions squash seeds being served by themselves, with gourd sellers also selling cakes made from the seeds, or the seeds being toasted, salted, fried, and/or covered in honey.
Given that these were staples foods, there were any number of variations and styles of preparing these foods. Things like dried squash flesh, bean flour, or stuffing either into tamales are all known to have been styles of consumption.
I would look into Sophie Coe's book America's First Cuisines. It's form 1994, but still has a lot of relevant and useful information. I would answer your question directly if I had my copy on hand, but I loaned it out. It should be a fairly easy book to get a hold of if you are interested. It also covers the Inca area, as well.