If a tree was on fire, how would it burn?

Generally they burn to nothing because they can continue to smolder for days. I have seen logs burn like a cigarette for several days.  If the fire goes out, what does not burn will remain.   Some charcoal and wood lumps is all that is left with the ash.   When you cut a tree, the stump is hard to burn.  To get rid of them, it is best to grind them out. Another interesting thing is that a beautiful tree, if it is cut down and gone, it really doesn't make much of a difference.  It does not ruin the view or composure.  It is easily forgotten.               

Context matters.

A tree by itself, no other trees around it, doesn't burn very well at all.  The leaves would burn off and maybe some of the outermost, smallest branches might catch but that would be it.  And it would have to be late fall or so; green leaves don't ignite easily.

In the late winter it's difficult to ignite a tree partly because it's cold and you have to get the wood hot enough to actually catch fire.  Again you might ignite the twigs but that would be about all.  As you get closer to the trunk the branches get thicker and have sufficient mass to resist igniting until the ignition source itself is exhausted and the threat has passed.

Occasionally you'll see a tree by itself burning with no other trees involved, but that's a tree that's burning from the inside.  Struck by lightning and split so air can get to the fire inside, that will go until the trunk collapses from the weight of unburned wood above.  Even then the entire thing won't burn to ash.

In a forest is another story.  You have trees closer together and if a fire starts on one, that heat is more concentrated: it's reflected back from other trees so the fire keeps going, and of course those other trees get that heat and some of those may catch too.  Now you suddenly have more than one source of heat and that ignites more trees, more heat sources and pretty soon everything's hot and it doesn't matter what season it is and whether the leaves are green, it's hot enough to melt wheels off of cars and there's so much heat you can feel it from hundreds of feet away.  A raging downpour would be required to bring a fully involved forest fire under control.

Entire trees will be easily reduced to ash in this context.  Rocks will split.  Roads melt.  It's pretty bad.

{General info ... so read up on forest fires, and the size and consisrency of Elder trees.}  Go up like firewood (i e fast and quickly)? No, unless it was a dried out snag (dead tree standing).  All wood that burns turns into smoke and ash; with charcoal and unburned bits left over.  Yes, water content matters, and a tree may split open (and sometimes even explode) when the water (sap) boils and makes steam ... but this may require a raging forest fire.