The two main things you need to build a decent fire and keep it going are oxygen and fuel. You'll need only to add a flame to get things started, but there is a knack to building a lasting, warm fire which does not smoke or smoulder.
If you are building a fire in a fireplace or woodstove, you should never use more than minimal quantities of evergreen wood (those trees which stay green all year round, also known as soft woods eg, pine, fir, cedar). These can cause dangerous creosote build-up in your chimney. Hardwoods such as oak, poplar, maple, walnut, cherry or apple are all good choices. Not only will hardwoods be safer to use, they also burn much hotter and longer than softwoods, and are therefore a more efficient source of heat.
If you use your fireplace frequently, you should have your chimney cleaned yearly by a professional chimney sweep who can also inspect it to make sure it has no structural problems or a build-up of dangerous creosote. The infrequent fire builder should also check the chimney before use to assure that no squirrels or birds have built a nest in the chimney, blocking the escape of smoke.
A mesh fireplace screen is essential for an open fireplace, as sparks can fly out and ignite combustibles several feet away when no screen is in place.
Green wood is wood that has been freshly cut from a live tree. When it has been allowed to dry in the wind and sun for at least six months it is then called seasoned wood. All wood has moisture, but green wood has as much as 45% moisture, while seasoned wood moisture is much lower at approximately 20%-25%. If you choose to use green wood, be aware that the fire will need to dry out the wood as it burns, reducing not only the heating efficiency of the wood, but reducing the size and beauty of the blaze as well.
In order to tell if the firewood you are buying has been properly seasoned, first check the ends and split edges of the pieces. If they are dark and discolored, this means the wood has rotted because of exposure to the weather for at least six months, and is therefore seasoned. However, this is not the only test, because some wood suppliers do not cut and split downed (dead) trees for firewood until they are ready to sell it, so the wood may be seasoned but still appear to be freshly cut and split. If the wood appears to be freshly cut and split, you will need to judge whether it has a 'fresh green smell' to it, and also whether the pieces are heavy for their size, indicating that they still have a large amount of moisture in them. Again, you can still burn unseasoned wood, but it will be more difficult to burn and you will not get as much heat from it.
If you are using an open fireplace, the fruit woods such as cherry and apple release pleasing aromas as they burn, and are often highly desirable for that reason.
Once you have acquired a supply of seasoned hard firewood to use in your fireplace or woodstove, you will want to store it properly in order to have it ready to use at any time. Wood that has been allowed to stand unprotected in the rain will be harder to burn than wood which has been protected from the elements under a tarp or roof. If you have no choice but to use wet wood, bringing it indoors and propping it near the fire for a few hours usually dries it out enough to make it easier to burn. In addition, if you are using the wood to heat your home on a daily basis during the colder months, you will want it to be conveniently located for easy access.
Building Your Fire
In order to build a good fire in your fireplace, you will need something to start the fire such as matches or a lighter, some kind of kindling, and wood.
First, make sure the damper in your fireplace is open, then place the kindling in the fireplace. Most people start with crumpled newspaper. In order to keep enough air flow (oxygen) supplied to the kindling, do not crumple the newspaper too tightly or it will not burn well enough to light your fire. Firestarters are an excellent alternative to crumpled newspaper and work very well if you've had the foresight to make some beforehand.
On top of the firestarter or crumpled newspaper, place small pieces of wood which will serve as the actual kindling, keeping enough space between the pieces to allow for air flow.
On top of the kindling, you can now place your firewood. You will want to start out with three pieces, arranged with two on the bottom and one on top, between, but supported by, the other two. If viewed from the side, they would appear to be arranged in a triangular shape. It helps if these pieces are split instead of whole round pieces, and are not perfectly straight, as little inconsistencies in the surface enable air to rush between the pieces keeping the flame going.
If you have built your fire correctly, you should see flames shooting up between the logs in places, and not too much smoke. To keep the fire going, add more wood to the fire before the logs have burnt to tiny cinders, or you will find that you need to start all over.