This story is probably the farthest you can get from canon while still staying sort of canon
Long story short, you're going to see things like Zuko leading armies into battle, Sokka executing prisoners, Katara decimating legions, Aang being nowhere to be seen, the Earth Kingdom being wiped out, almost everyone's forgotten about the legend of the Avatar, and really different nations.
For example:
The Air Kingdom- A large mountainous continent. Most cities are inexplicably hovering, and the people inside won't share their secrets.
The Fire Colonies- Ragtag nation of fiery people that live to the south and north, they're at war with the Water Empire
The Water Empire- Empire for short, this is a nation of cold, heartless people hell-bent on dominating the world. Currently indifferent to the Air Kingdom, they'vefocused on the reclusive Fire Colonies to wipe them out, but are having a hard time doing so. Still cocky from wiping out the Earth Tribes.
Earth Tribes- Tribes of people that lived on spires of rock that pierced the oceans, these people were wiped out. Supposedly some survived, but not many.
Anywho, carry on!