One reason to have a a wood stove to cook with in addition to a gas one is for cooking beans. Cooking dry beans takes many hours, and would be too expensive and impractical to cook using gas, so many families cook large batches of beans over a fire in order to save on gas. Below are some pictures and step by step instructions for starting and using a cooking fire.
Your stove may look something like this. A wooden stand with a box on top filled with sand (to prevent the fire from spreading to the stand/box) and some concrete bricks to contain the fire and also to set a grill or a large pot on above the fire. Its also important to have airflow and easy access to the fire for adding/removing sticks.
Just like starting any fire, start with a pile of small thin dry sticks or kindling, maybe some bark or paper scraps if you have them. Its a common practice also to burn pieces of plastic to get it going, although you may prefer to stick with tree bark.
Gradually add more until you have a decent flame going, then when ready put in some larger pieces of wood. Its good to use long sticks, so that one end can be burning and you can handle them by the other end to move them around without being burned.
Fan the flames with a lid to get it nice and hot.
And now you're cooking with wood!