Not all of the kingdoms practice burial customs.
In Tiranoci culture, it is very important that you are buried in your family's ancestral lands alongside your forebearers, which can cause some trouble when your family are former colonists that followed Caradryel's Edict of Evacuation and said lands are populated by humans.
Ellyrians also bury their dead, but instead of focusing on ancestry each elf has a pre-designated grave, where all of their companion animals are buried (should they die while the elf is still alive). They believe that when the elf has died and been placed in the proper grave, their soul alongside those of their companions travel together to Kurnous' side.
Yvressians build elaborate graves, but they are not so fussy about geographical location- rather, it should be a site that bears importance to the departed, such as the spot where they were married, where they won their greatest victory, and so on, which can be anywhere in the world.
Nagarythians believe that once the soul has left the body it is just an empty vessel of meat and bone, and show an unsettling disregard for the corpses of their own fallen.
Burial at sea is practiced in both Cothique and Eataine, but where the latter construct elaborate funerary vessels that are cast adrift on the waves, Cothiquans just toss the bodies into the ocean to give back that which they have taken from it all their lives.
Caledorians believe that the soul is trapped within the body after death, and must be freed by burning it- preferably in dragonfire, of course- and then scattering the ashes to the winds.
Sapherians hold many similar beliefs, which some historians attribute to the influence of the Dragontamer, but instead of burning the body they simply conduct a ritual that converts it into raw magic, which is then carried away by the Winds.
Chracians also burn their dead like the Caledorians, but for a more practical reason: the smell of elven flesh has a tendency to attract the beasts of the deep forests. Once cremated, the ashes are then placed in a clay jar and buried.
Avelornians place their dead in great caverns beneath the earth, arranged on thrones of stone and clad in the same clothes that they wore whilst alive. It is customary to visit them from time to time and tell them of what has gone by since they died, and it is rumoured that sometimes they even speak back.
And, of course, there are regional variations within the kingdoms and colonies that have their own customs, either following the kingdom which originally founded them or with their own twist on things.