To prepare and build a fire, you need three types of wood:

Tinder

The most important element to starting any fire is tinder. Without good tinder no amount of spark or friction-produced ember will be useful. Tinder comes in many different forms from natural to synthetic and may or may not include additives. This is the base fuel needed to start your fire and it will provide the first flames which you’ll apply to your kindling.

Straw, dryer lint, and wood shavings can make good tinder.

To make tinder, collect what you can from small bits of dry leaves, straw, and extremely thin pieces of wood, about the size of small wire.  If you you have firewood the size of fuel below, small pieces that can be manually pulled away from the firewood can serve as tinder.

To create wood shavings, locate a small dead and dry branch.  While holding a knife at a right angle and with the blade pointing away from your body, run the blade away from you along the stick to create the shavings

Fuzz Sticks can also be used as tinder.  

Kindling

The second element of producing a sustainable fire is kindling.  Kindling provides the first base of flames strong enough and long-lasting enough to light your main source of fuel.  Kindling can be collected from dry twigs about the size of pencil, or it can be cut from thick branches about the size of your wrist, or pieces of fuel wood using an axe or possibly a hatchet.  Whenever handling an axe or hatchet, be sure to use gloves and eye protection, be knowledgeable of proper usage of an axe or hatchet and apply caution.   Videos below describe methods for making kindling.

Fuel Wood

Fuel wood is the last ingredient for your fire and is any large piece of wood that is used to feed and maintain a fire.  Now, you might think about dragging over some giant logs, but the truth of the matter is that good fuel wood generally doesn’t need to be larger than the thickness of your wrist and the length of your arm.   That can be collected from large, fallen branches, and then cut with a saw or axe into sizes that can be used in your campfire.

More often than not, you're going to purchase your fuel wood.   When it comes to actually preparing fuel wood, you will need to locate large dead branches where you are camping, or you will have to have cut and split felled trees as well as allowed the wood to dry before you need it,   Being a good steward, you don't want to cut or attempt to make fuel wood from a live tree.

If you do have trees to cut and split and time to allow it to dry into quality fuel wood, then a splitting wedge and axe can be used.  The videos below describe how to split wood into fuel wood.