A few materials and a simple technique are all you need.
MATCHES: Wooden kitchen matches (or long fireplace matches for deep hearths) are best. These burn more slowly than paper matches, giving you time to ignite the tinder before the match burns out.
TINDER: The first element to catch fire, and the first to burn up, tinder can be composed of newsprint, brown bags, wood chips, birch bark, and the feathery tips of dead pine branches.
KINDLING: Place kindling, finger- to wrist-thick sticks and branches, on top of the tinder; they stay ablaze long enough to set fire to the logs.
DRY HARDWOOD LOGS: The harder the wood, the longer and hotter the fire will burn. Dry wood also minimizes smoke and ash. Green (freshly cut) wood is full of water, and it burns unevenly. Oak, maple, ash, beech, and birch are good choices; for fragrance, try logs from cherry, pear, and pecan trees. Softwood logs (from trees such as pines and spruces) burn very quickly, and their resin never completely burns off; instead, it pollutes the air and collects on chimney walls. It's best to save softwood for tinder and kindling.
Crumple sheets of newspaper into balls the size of grapefruits, or twist them into batons, and place them on the hearth. Above and around the newspaper, lay several small pieces of wooden tinder and kindling, in a crisscross pattern (leaving air space between the sticks). Take a lit match to the paper. Within a minute, the kindling should be burning steadily. Lay a couple of thin, split logs above or beside the flames (but not directly on them). As the fire begins to blaze, you can add a few logs at the same time, but always leave at least an inch of space between them. This creates a natural bellows: As the warm air rises up the chimney and into the room, cool air is sucked up into the spaces between the logs, fanning the flames. Don't overfeed the fire, however, or the force of the rising heat can send burning embers up the chimney and onto the roof.
A split oak log releases lots of heat but not much smoke and ash for its size. Fruitwoods are fragrant fuel; their knots burn slowly, and the chips are good tinder.
Kindling such as pine and birch sticks burns long enough to allow small logs to catch fire. Dry corncobs make good kindling, especially when dipped in wax.
Fatwood is "designer kindling" -- highly flammable resin-laden sticks from coniferous trees. Hemlock twigs, birch bark, and newspaper make excellent tinder; they burn quickly, spreading the match’s small flame to the kindling.