It is useful to know something of endgame theory - for example knowing who has the opposition.
Diag.1: Whoever moves given an ODD total of squares between the kings
does NOT have the opposition. So if White to move (and 5 squares) Black
has the opposition.
Diag.2: EVEN (4sq.): Mover has the diagonal opposition.
Diag.3: Whoever moves given a RECTANGLE of SAME COLOURED CORNERS
(ie. f4-f8-g8-g4) does NOT have the opposition (eg. 1. Kf5 Kh7, Black keeps
opposition).
Diag.4: DIFF. COLOUR CORNERS: The mover has the opposition (eg.
White to move keeps it by 1.Ka2).
Basics
Basics - Endgames Overview
Endgames 5 - Blocked Pawns