One can try to imagine what a meal would have looked like for, say, an Anasazi farmer living in modern day New Mexico a millenium ago, based on the local plant and animal life, and maaaaybe on what the dishes of more recent indigenous peoples were like.
But how can archaeological remains help us to learn about traditional cuisine and cooking techniques? Is it typical to find specialized cooking tools (along the lines of a mandolin, colander, or whisk) in ancient cultures? Do marks left on kitchenware give us useful information on food preparation (scratches could indicate using knives to cut food, for instance)? Traces of minerals or proteins left behind that indicate how heavily spices or salt may have been used, or how often certain ingredients were combined?
You're on the right track. Marks can be left on bones from teeth and knives; some recovered skeletons had marks on the teeth indicating that they likely ate the meat raw or barely cooked and used a knife to try and saw off pieces while it was still in their mouth.
What makes it difficult is that very little can actually survive for this long without unusual preservation methods, like the "bog bodies". Wood, cloth, furs, reeds, and other soft materials rapidly decompose until only bones, stone, and metal are left. It's also virtually impossible to identify the purposes of some items accurately, as a simple item like a bowl or bone needle could have many different potential uses. There could be all manner of items that were used for cooking but never made it to the historical record because they were made from materials that wouldn't be naturally preserved for tens of thousands of years.
Here is an answer of mine that directly discusses Puebloan (the term "Anasazi" isn't in use anymore) cuisine. I don't go into tremendous detail on how we know these things from the archaeological record, but I discuss some of that aspect. For instance, the roasting pits I mention that are used for roasting agave hearts are found archaeologically and are very similar to roasting pits used in historically documented periods.
Let me know if you have any follow-up questions.