To light the fire you need to use either a wood log or wood branches with the fire (Use with icon, closed fist). Using the Fist Tool click on the wood in the inventory window, then click on the fire pit to add the wood to the fire pit.
You can add multiple branches or logs to the firepit before lighting it. Keep adding wood after the fire is lit, to keep it burning. Logs burn much longer than branches, so if you need to cook a lot, use logs.
After you have put the logs on the fireplace, light the fire with a Fire Essence, again using the Use with cursor. Using the Fist Tool click on fire essence in the inventory window, then click on the fire pit.
Fire is used to cook Raw Meat into Cooked Meat, use the meat with the fire (you will get a message that you cooked the meat). Using the Fist Tool click on the raw meat then click on the fire pit. To speed the process up, hold down left SHIFT key while clicking on the fire pit, in this way you can cook the meat pieces without moving your mouse.
One log only stays lit for a short time, so additional fuel is required to cook large quantities of meat. Often wooden logs will be found acting as benches around firepits.
Frying Pan use
A Frying Pan can be used to cook 10 Raw Meats at once. You need Human Nexus 2 to use it. Wield the Frying Pan (equip the frying pan as you would with weapons or clothing) and cook the meat the regular way using it with the Use with icon on the fire. In this case the Fist Tool will pick up and cook 10 Raw Meats instead of just 1.