How did the American tradition of trick-or-treating on Halloween begin?

Answer 1

It comes from the older practice of guising and souling in Scotland/Ireland and England.

Halloween being the night when the walls between the living and the dead worlds were thin and souls could walk the earth.

Souling is the practice of saying a prayer for the dead in return for a small present,

Guising is rooted in the Celtic purification rituals - Guisers would go round dressed up as evil spirits and perform some small performance (originally to pacify spirits later just a party piece) in return for a gift.

Emmigrants took this to the US (The Colonies) where over time it changed.

In the UK this tradition to some extent got tangled up in Guy Fawkes night on the 5th Nov with it's accompanying "Penny for the Guy" and Bonfires (although fire was a big part of the older pagen festivals) and is being gradually weakened by the American version of demanding gifts for NOT doing a trick.