How to think in chess?

Books are written on this subject

GM Larry Evans' method of static analysis - Chess Forums - Chess.com

Look for checks and your good to go

You mean:

"Always give check... it MIGHT be mate!"

Very true as well, always check, might be mate!

Knights should go forward.

Bishops can be used sideways, though.

Visually. Each piece with it's own territory.

@1

"How should I think in chess?" ++ It is an elimination process. Select 3 candidate moves. Calculate what will happen after that. Evaluate the position at the end of that line. Decide. Blunder check.

"What do I look for?" ++ Checks, captures, threats

"How do GMs think in the board?" ++ Think like a Grandmaster - Kotov

'When my opponent’s clock is going I discuss general considerations in an internal dialogue with myself. When my own clock is going I analyse conctrete variations.' - Botvinnik

Hikaru Nakamura's videos on his games in the Candidates give some useful insights into how the top players think.

I also recommend buying this book: https://www.danheisman.com/the-improving-chess-thinker.html

Check out this book: https://www.amazon.com/Grandmaster-Preparation-Positional-Jacob-Aagaard/dp/1907982264

It simplifies the process into 3 things:

1. Weaknesses
2. Pieces
3. Prophylaxis