How to make a fire without burning the ground

Well, insulating the floor from a campfire, which usually has 900-1200 degrees Celsius and burns for several hours, is quite difficult. The soil itself does a decent job, but of course that's the part that you don't want to burn... Restoring life to a scorched patch of soil will take a while, but relatively speaking a couple of scorched patches won't make much of a difference to a big forest. I would guess that collecting garbage or some other efforts would help the forest a lot more.

There's two schools of thought here that I know of - the first is to avoid lighting a fire where there's ground you could easily damage, and the second is avoiding the heat getting to the ground. Combine both if you can. As far as the first goes, I won't say a great deal about that because beyond the obvious (being open minded about where you camp and looking around for a good spot) there isn't much else that can be done. As far as minimising the heat getting to the ground, when I want to take this approach I generally pile rocks on the base of the campfire, then light it the fire on the rocks. It's not a foolproof approach, and rarely leaves the ground completely trace-free, but it's a darn sight better than the mark you get just having a bare fire on the ground.

If you are looking for a cooking system for backpacking the http://www.traildesigns.com/stoves/caldera-sidewinder have the option of using a titanium floor for this exact purpose. In the interest of facilitating Leave No Trace wood burning practices, Trail Designs offers two styles of titanium floor plates to go under your Ti-Tri systems. The "split floor" is designed to go with the standalone Sidewinder, or the single piece floor is optimized to be used with the Inferno. These stoves are for small twigs burning and works great as a cooking system. However, I do not have experience with their floor plates. As for the 'Inferno' it does a good job at fully burning the fuel/twigs and only leaving ashes.

I'm not sure what you are afraid to destroy with you fire. You should remove any plants around the fireplace anyway. The bigger problems are the remains of the fireplace, such as partially charred logs, which can stay there for months. They are more an aesthetic problem, and they will be eventually utilized by the nature, but it takes much time. From my experience, if you let the logs burn completely, and you'll scatter the ashes, the remains of the fire will disappear very quickly. If you extinguish fire with water, they will hold log. Of course, you can scatter the ashes only when they are cold, for example the day after (in winter you can do that quicker, since you can throw them into snow, reducing fire risk to null).