Wood fire-building:
In a fireplace, before you start the fire, it helps to light a section of kindling or primer paper (newspaper, for example) and hold it up inside the flue for a few seconds (watch your fingers!). This starts to warm the column of air (which is usually cold if the fireplace has been dormant for a few hours) already inside the flue. Excessive cold air in the flue traps smoke from the logs, sometimes forcing it back into the room, even if the flue is open. Warm the air in the flue, and the smoke flows out nicely, reducing the risk of smoke inside the room.
General fire building at a campfire or in a fireplace: arrange the kindling first, in a slightly pyramidal shape, instead of flat. Then arrange the logs in a similar fashion, leaning together at a common apex, over the little kindling pyramid. It's usually good to start the fire with smaller logs at first (around 2-3" diam., say, and obviously make sure the timber is dry), so that it can catch, before adding larger logs later. The sloped shape of the logs helps the flames course upwards along the length of the wood for a better burn that consumes more fuel and leaves less "dead" spots on the wood. It also ensures nice airflow between the logs, which is critical to a successful fire. Just make sure when arranging the logs that, when they "settle" (fall as they lose material consumed by the fire), they do so toward the center of the fire, and back toward the brick, not forward into the room! This is a great way to build a good fire (don't use liquid fuels as a starter!).
If you don't have a bellows, you can make one very easily, with a section of metal pipe (not plastic), around 3/4" diam., with a threaded end. Attach a "mouthpiece" section to the threaded end that just fits your lips, the way a mouthpiece on a trumpet, trombone, or other brass instrument works. The pipe should be no less than 3' long. Hold the pipe with both hands, and blow down the length of the pipe; the narrow diameter focuses your breath in a very tight area, allowing you to bellows specific areas of the fire (where the embers are) in order to rekindle, and you don't have to get too close, or wind yourself with excessive blowing. It also helps reduce the amount of water vapor you pour onto the fire.

Obviously, the metal of the pipe should be something it's o.k. to put your lips on (never lead!).
More as I think of them,
Warrior Poet