Slate has a fun story by Andrew Lawler that covers some of how we study ancient diets: "The Mystery of Curry":
Examining the human teeth and the residue from the cooking pots, Kashyap spotted the telltale signs of turmeric and ginger, two key ingredients, even today, of a typical curry. This marked the first time researchers had found unmistakable traces of the spices in the Indus civilization. Wanting to be sure, she and Weber took to their kitchens in Vancouver, Washington. We got traditional recipes, cooked dishes, then examined the residues to see how the structures broke down, Weber recalls. The results matched what they had unearthed in the field. Then we knew we had the oldest record of ginger and turmeric. Dated to between 2500 and 2200 B.C., the finds are the first time either spice has been identified in the Indus. They also found a carbonized clove of garlic, a plant that was used in this era by cooks from Egypt to China.
It's a nice piece. Paleoanthropologists are using similar techniques to probe the diets of Neandertals and other ancient humans. It will be a lot of fun when we can compare a wider variety of ancient cuisines.