The open flame is the oldest cooking method in the world. Every culture does it. The only real difference is in the ingredients and how the fire is used. In Mexico cooking fires are made with Mesquite wood ringed with stones. Before the Spanish brought iron, food was suspended on green sticks or placed on flat stone in or near the fire. After the Spanish, small cooking grates were used to place the food directly over the flame.
Like any culture the Mexicans cook what is easily available like fresh fish, lamb, bananas, tortillas, and lots of chilies. The first ingredient however is the wood. Mesquite is readily available throughout most of Mexico and is the wood of choice. Though most of us might not have Mesquite growing in the backyard, Mesquite charcoal is abundant all over th world these days. So if you plan on cooking some Mexican dishes on the grill, first go out and get some Mesquite charcoal for your charcoal grill or Mesquite wood chunks for the fire box of your gas grill (see Making Smoke).
The second basic ingredient in Mexican cooking is Salsa and Recado. Salsa means sauce and it is what you serve with the meal. It is meant to be added after cooking. Recado is a marinade used to season food before and during cooking. Recados are typically spicy pastes or dry rubs. They provide a deep rich flavor to food just the way traditional barbecue dry rubs are used on steaks or other meats.
The Key ingredient to almost any Mexican dish is the chilies. There are more than thirty different types of chilies used in Mexican cooking and the true expert looks for not only the type but the region it was grown in and how it was prepared. Chiles come dried, crushed, pulped or fresh. If your not sure of your chilies don't try an substitutions. There is a wide range of heat from differing chilies.
Other typical ingredients in Mexican cooking are: coconuts, bananas, cilantro, cumin, all kinds of tropical fruits, garlic, and banana and avocado leaves. Banana leaves are used as a cooking surface. The oils and anise flavor permeate foods while they cook give a wonderful flavor. If you want to try it, get a couple of banana leaves, wash them and place them directly on your cooking grate still wet. Put whatever you are cooking directly on the leaves immediately. Typically this is done with fish like my favorite, red snapper.