If it burns out, it can be relit using Wood, Mucus, Twigs, Dry Herbs, and Tree Saplings. Open your inventory, click one of the aforementioned items, and hold it over the fireplace. When the cursor turns into a plus sign (+), click the fireplace.
It can be dismantled using a Hammer.
To cook food, left click items from the inventory and hover over the fire as if to drop it. When the cursor turns to a "+", left click on the fire to kindle it or cook food.