In a place far enough away from flammable structures and trees (including tree roots), a place that is sheltered from strong gusts of wind, dig a shallow pit (you only need to go a few inches deep) a few feet larger than you want your fire to be (if you can, it is best to dig a bit deeper and then fill the pit back up partways with sand). Encircle the perimeter of the pit with rocks or bricks. Have buckets of water, sand, a fire extinguisher, or what not, on hand at all times for safety and to put out the fire when it's all over.

Now gather:

• Tinder:
  lightweight and thoroughly dry material that burns well and quickly and that allows larger sticks to ignite. Try twigs, shaved wood, dried leaves, paper, bark, grass, dried pine needles, broken up pine cones, dried mosses, the heads of cattails, dryer lint, string, etc. You can also use some charcoal briquets.
   

• Small kindling:
  thoroughly dry sticks that are thumb-sized in diameter
   

• Medium kindling:
  thoroughly dry sticks that are about wrist-sized in diameter
   

• Fuel:
  Larger logs that are thoroughly dry (oak, maple, ash, beech, and birch are the best for burning)

If you use charcoal briquets, make a flat bed out of them at the center of the pit. Top them with a large ball of other tinder material or, if you're not using briquets, just put the tinder in a pile at the center of the pit.

In any case, take the small kindling and make a teepee -- a standing triangular structure -- to surround the tinder, setting up the sticks at 45 degree angles from the ground and leaning them against each other in the middle. They can be lashed together at the tops, and their ends can be sort of driven into the ground a bit to keep them steady. Leave enough gaps to allow oxygen in toward the tinder.

Now build a cabin around the teepee. Lay two of the medium-sized kindling sticks parallel to each other on either side of the teepee. Then lay two more on top and perpendicular to the first two. Then lay two more on top perpendicular to the last two, and repeat until you've built a structure that is 5 layers high. Make sure the larger logs are toward the bottom, and the smaller ones are up higher.

Drop a lit match inside the teepee (using a candle to light it will keep your hands away from the flames and may be less frustrating if the matches keep going out). As the fire burns, add more wood as needed, going from smaller to larger pieces as you go.

When the fire is over, pour water over it and pile dirt on top.

For Colorful Flames

If you want colored flames, you can do the following -- but it must be prepared well in advance:

Pick the color(s) you want your flames to be and get the chemical(s) needed to produce the effect. Chemicals can be gotten locally (sometimes from stores that deal with fireplaces) or online, such as from this place http://www.chemistrystore.com/ (offsite, will open in new browser window). You only need "technical grade" chemicals, not the more expensive "purified grade.":
 

 
Wear rubber glovers during this procedure. Now, add the chemical(s), singly, to a plastic container of water for each flame color -- adding as much as the water will absorb (about a half a pound per gallon of water).

Soak your wood, "logs" made of tightly-rolled newspapers, or some pine cones in the solution(s) overnight (you can also use sawdust to sprinkle onto fire to make briefly burning colored flames. Just stir some liquid glue into the liquid, too, and then add the sawdust. The glue will allow chunks to form).

Take the wood/cones/sawdust out of the liquid, lay out on newspapers, and allow to dry thoroughly (for sawdust, spread out onto sheets and dry). Save the newspapers on which they've dried, and roll them up tightly to form "logs," too, as they can produce pretty colors from the chemicals they've absorbed.

Just throw these things on to your fire for pretty flames (can also be used on indoor fires, but ventilation should be good). The chemicals can be thrown directly onto the fire, too, for short bursts of color.