My American flag had a hole in it (presumably from a falling branch) and appeared very worn. Nylon flags, when flown continuously outdoors, generally last less than a year. This is why most government buildings remove their flags at sundown and raise them at sunup.
Remove the flag from its flagpole and fold it into a triangle. Do not let the flag touch the ground.
Build a campfire in a safe area and wait for the coals to get hot (think "cooking" hot).
Carefully place the flag in the center of the fire. I say carefully because you want to be able to collect all of the flag ashes later. While the flag is burning, it is customary to recite the Pledge of Allegiance.
Wait until the flag material has been completely converted into ash. Then, you can either wait for the fire to go out on its own or use a fire extinguisher to put the fire out.
Bury the flag in an area where people won't often walk over it. It is also customary to leave a marker of some kind to mark its location.
And of course, after disposing of your old flag, be sure to replace it with a new one!