White to move
I ) ( plain ) Calculation ( using the knowledge we are looking for 1# )
1) Ra2, no check
2) Rb1, no check
n) Nd6 check. Is it mate? Can i take the rook? No.... Can i move away? Ke7 still check Kd8, no check
II) ( almost plain ) Pattern recognition. This is a typical KRvK Endgame posiition ( if you can "substract" all other pieces! ). This method narrows the vision to a few pieces.
III) ( plain ) Board Vision
Board Vision ( = Chess Board Vision = Chess Vision = Board Awarness ) is the recognition of "whats going on at the chessboard" now. Without "seeing" whats going on now you cant see "it" in the future either.
We see that the black king has 3 squares d8,e8 and f8. Only 2 pieces can attack such squares at once, rooks and queens. Now you look along this rank and intersect with the possible moves of the white rooks and Queens. The intersection is at h8.
There is a wonderful explanation of the benefit of advanced Board Vision --> here! <--
The method ( (motor) skill ) of "intersection" is explained in GM Maurice Ashley's Book: The Most Valuable Skills in Chess , which is a wonderful explanaition to his "Skill Trainer" , but i realy dont think that this book is interesting for the average chess beginner.