How do you carbon date something that has been burned? It seems like that would mess up the carbon compounds and throw off the results.
Nope---it is the RATIO of C14 to C12 that matters. Mere burning won't change that--the remaining carbon will still have the same ratio of isotopes as the original wood.
Charcoal is almost entirely made of Carbon... So you can measure the ration of C12 to C14. However, the theory behind carbon dating ignores potential variables that could effect it's acuracy. Kind of like if I measured my nephew's height over a year's time, then calculated how long it would take for him to double his size, and then "scientifically" calculated how long ago he was two inches tall. (That's a hyperbollic analogy, but you can see it makes assumptions and ignores variables that effect the acuracy of employing that method.)
Radiocarbon dataing is not very usefull in actually determining the age of material with much degree of certainty... Despite this fact, it's still employed as a propoganda tool knowing most people don't know any better.