The easiest, but slowest way to get a bed of coals is to build a huge log fire and wait a few hours. This takes the least effort and the most wood. To get quick efficient coals, burn small pieces of wood. In boy scouts, the rule is to find wood (or split it into pieces) the diameter of your thumb. These are neatly stacked next to the fire and added as needed to maintain a constant temperature. When cooking directly on the coals, the new wood is added at one end of the fire and the coals are pushed down into the cooking area. If you are using wood that doesn't make coals, you need to add pieces very often to maintain any heat.
Fire pit construction varies according to weather conditions, wind direction, what and how much you are cooking and the type of fire wood that is available. Once your fire is started the two important things to manage are fuel, mentioned above, and air flow. If you are building a fire in a windy place such as the grassy plains of the Dakotas, you need to dig out a deep fire well.
The extreme version of this requires two holes dug about a foot deep and a foot apart. They are connected at the bottom by a tunnel. A pot or grill (or big piece of meat) can be placed over one hole, while the other provides access for fuel and air. The Dakota fire is also very efficient, requiring less fuel, as almost all the heat is put to work. Moderately windy conditions can be handled with a wind screen of rocks or logs.
My standard cooking fire is dug down about four to ten inches, depending on soil type and wind. (Save the soil and sod if you can to put back when you're done.) If the wind is not too strong, line up the pit so the breeze flows parallel to it. Make sure the wind isn't blowing the smoke to where you want to sit while you cook. The pit is then lined with the flattest and driest stones I can find, including the bottom. Stones that contain moisture tend to explode as the water becomes steam. The stones come up another four to six inches above ground level.
If I am going to do a pit roast, another, deeper pit is dug a foot or so past one end of the main fire, and the hump of dirt between the two is not rock covered. Pit ovens should be dug deep and wide enough to accommodate a stone lining and a green vegetation lining as well as the food. The area between can be used to generate coals to replenish the cooking area, heat rocks for stone boiling or covering the baking pit. The length of the fire varies according to the number of people cooking, the width is from one and a half to two and a half feet. One or two people can easily cook on an 18" round fire.
Extreme case one: you've got mainly big dead trees to burn. Solution one: the star fire. Trim off the side branches and stick the ends of three or more trunks into the center of the fire. Keep pushing them in as they burn. Solution two: a moving fire. Lay two trunks parallel, a few inches apart, and build a fire at one end. The fire will work its way down the logs. Solution three: build a fire against the log and burn it through, then proceed as in one or two above.