It may be a little more complicated, but it's what I grew up with.
It Divides the board into King side and queen side. The square that the king sits on is King 1. The pawn in front of the king is the king pawn and is setting in king 2. My opponents king is setting on my king 8.
The Bishop net to the king is the kings bishop and is setting on kings bishop 1 (KB1). The Pawn infront of the Kings Bishop is the Kings bishop pawn and is setting on Kings bishop 2 (KB2). My opponent King Bishop is setting on my KB8.
The complicated part of this is that my king is setting on my opponents king 1(K1). My opponents K5 is my K4. (can you believe I perfer that?
The way it looks is like this:
P-K4 P-K4 This reads Pawn to king 4 Pawn to king 4
P-Q4 PXP Pawn to queen 4 Pawn takes pawn.
Castling king side is 00 Castling queen side is 000
This is a brief description, but you get the idea.