This is not really a Texas chili recipe, but an overview of how to make this Texas original. There are no set number of cups of this or teaspoons of that. This guide to making chili is to help you get a feel for how this dish is made, and then go from there and design your own pot of delicious chili.
In your favorite large pot (preferably cast iron), throw in some meat. Remember that chili is a meat dish, and not a stew or soup, so meat should be plentiful. It is usually beef, but some people love venison, pork, chicken, or even rattlesnake in their chili.
Most chili cooks use cheaper cuts of meat, since it benefits from slow cooking. Cut the meat into about 1/2 inch cubes, or have your butcher grind it coarsely. Never use hamburger meat, as it can become mushy. You want texture in your chili.
Brown the meat in a large cast-iron pot (preferred over anything else). Drain off any excess fat.
The chile is where your chili will get its flare, so the right chile powder is crucial. To make authentic chili, grind up your own dried ancho and/or New Mexican chile pods. If desired, do the same with pequin, cayenne, or any other hot chile pepper if you like more heat.
The pros usually toast the chile pods in a skillet or in the oven. You are welcome to use packaged chile powder, which contains chile powder and other seasonings. Just understand that your chili will not be as flavorful.
The meat and chile powder simmer, with a liquid, salt (to taste) and black pepper (to taste) in the large pot. The liquid is up to you. Some like to use just water, while others prefer beef stock or beer. Others even use black coffee as their liquid of choice. The main thing is to be careful with how much liquid you use, so the chili does not become runny.
After simmering for a couple of hours or more, if the chili is still runny, you can thicken it with masa harina, or corn flour. Some people add this just because they like the extra flavor and texture it adds to chili.
Add spices throughout the simmering process to create "layers" of flavor. The main spices to use are garlic, cumin, and oregano.
Original chili cooks never added onions or tomatoes, but they are common today. If using onions, mince the onion in very small pieces. If you want to use tomatoes, think about leaving Texas and cook your chili elsewhere.
To make real Texas chile, never add beans to your chili. The preferred way is to serve beans on the side, where you can add them to your bowl of chili, if you want. There is probably a law in Texas that addresses putting beans in the pot of chili.
A good (and not so good) cook can make a great pot of Texas chili from these guidelines. Just taste the chili regularly, and add the spices to taste along the way. All great champion chili recipes started this way, using no strict rules, and using common sense and taste.