Right I really struggled with figuring this out so figured I'd write out a step by step guide for cooking, hopefully it will assist some people.
1. Create a fire place:
To do this use an axe of some description on a tree.
Aim at the tree and hold RT. This will cut it down after a few circle cycles. This will then produce some sticks and some wood logs on the floor.
Take either a rag, bandage or bark into you hand. Whilst you have one of these items in you hand, place cursor over the sticks on the floor (or go into inventory and highlight the sticks in the vicinity and press B). You should be given the option to press RT to change recipe (make sure this says fireplace) or hold RT to craft. So hold RT and you will craft a fireplace.
(To get rags use an axe/knife on any item of clothing. To get bark use a knife in you hand on a tree and press RT).
You will now need to add fuel to the fire otherwise it will not burn for long. If you build the fireplace where the sticks and logs fall from cutting the tree I think they automatically go into the fuel. If not you have to pick up the logs and put into your hand then use the RB and RT buttons in the inventory screen to highlight the 'fuel section of the fireplace. Once you have highlighted it press B. This should add the logs to the fireplace.
2. Light your fire:
To light your fire you need a box of matches or a hand drill kit.
With matches just put in hand and aim at fireplace and press RT
to make a hand drill kit, get some bark in your hand and highlight a stick (from the tree) in the vicinity or inventory. then ensure the right recipe is selected and hold RT.
3. Putting meat on a stick:
This needs to be a stick from a BUSH! use an axe to get one of these and should drop a long branch. Put this stick in your hand and press B on any meat in your inventory. (to get meat kill animal and use a knife to skin it will drop meat).
Cook the meat on a stick and enjoy.
Hopefully this was all correct I did it from memory!