Does a pawn transitioning in the Promotion Square work from that square or begin action from the original square of the piece it chooses to become? That is, if it becomes a queen does it go back to the square where the queen started?
The promoted piece replaces the pawn on the square that the pawn moved to (the 8th rank for White, the 1st rank for Black).
From the FIDE Laws of Chess, (emphasis mine):
3.7.e. When a player, having the move, plays a pawn to the rank furthest from its starting position, he must exchange that pawn as part of the same move for a new queen, rook, bishop or knight of the same colour on the intended square of arrival.