Choose a location that is free from tree roots. Sand is the best substrate to build a no trace fire upon. If there is sod, dig down at least 3-4 inches and set aside the sod. Lining the edge of rocks is up to you; rocks hold heat and reflect heat back towards the fire, making for a hotter fire, but the flames may blacken the rocks.
Gather a large quantity of small twigs, finger-sized branches, and wrist-sized branches and keep them in separate piles.
Begin your fire with the small twigs, but keep half of the twigs aside. Build up your fire with larger sticks until you are using the largest wood that you have and maintain the fire with large wood.
An hour or so before you are ready to put the fire out, start decreasing the size of the wood that you add. As the fuel size diminishes, occasionally stir through the ashes to bring up to the surface any unburned coals. By the time you have finished burning your last small twigs, you should be left with a pile of fluffy ashes, but no partially burned wood.
If the forest is wet and there is absolutely no risk of forest fire, I often scatter the ashes. Otherwise, pour water over the ashes and replace the soil and sod (if you are camping for more than a day, remember to water the sod). If you lined your fire with rocks, scatter them with black side down.
Within a few weeks, your campsite should be indistinguishable from the surrounding forest.