Most recipes call for rice with chicken livers and/or gizzards. Some people use ground meat or game; onions and peppers typically round out the dish.
A bone of contention with dirty rice comes between those who cook the rice with the meats and vegetables and those who cook them separately and mix them with seasonings before serving. I belong to the cook-separately-and-mix faction. I do the same with jambalayas. I’ve been called to the carpet for that more than once, but I stood my ground. I like the texture better.
For dirty rice, first cook your gizzards. You can go to the trouble of trimming the membranes if you want, but I’ve found that if you stew gizzards for a very long time they’re going to end up as tender as can be, easy to mince, and the resulting broth is a thing of beauty.
Sauté trimmed livers with a little garlic and minced white onion until just done through. Add chopped meats to cooked rice with whatever sautéed vegetables you like with a little oil to moisten.
Season to taste. I like an Italian herbal blend with a little black pepper. Keep warm in a covered container, and add chopped green onion before plating.