I've become a life master without using any formal thinking process. But I have not been able to break the 2300 barrier after trying for 25 years. So I've become interested in this topic lately.

It seems to me that any formal process would have two steps. The first goal is to eliminate bad moves, the second goal is to select the best remaining candidate. Because there is often a choice of equally good moves, I think the first step is the more important one.

I would suggest five questions to help eliminate bad moves:

1. Why did he make that move? Note that there can often be more than one reason. If your answer is "he moved his queen to defend the pawn I was threatening" you may be missing "... and also to threaten to take my bishop."

2. Does he have a tactical threat? You always have to look at the checks and captures.

3. Is the move I am about to make feel obvious and natural? The move that feels wrong usually is.

4. After I make my intended move, can I safely meet all of his obvious replies? You have to ask this question on every move. I have also seen this described as, am I missing an obvious tactic? 

5. Does my intended move fit in with my mission statement? This requires a bit of an explanation. Often during a game I ask myself how I intend to win this game. My reply to this question becomes my mission statement. I try to make moves that fit with what I am trying to do. For example, my mission statement may be "I want to make noncommital moves until my opponent runs short on time, and then complicate the game. My opponent will then make a blunder" or "I plan to trade several pieces, win his a and b pawns, and then queen my c-pawn."