What's your process for finding the best move?

I'm speaking of daily chess that you can take 2 days a move on but any style is fine.

I will edit this comment because CB deleted his comment. Anyway, my advice is to think as logically and as simply as possible. I won't offer you any exact method, I'll let other people who know better do that. I don't advise spending a lot of time on moves just for the sake of it. If you're getting nowhere, just make a move. Don't waste time. Just to be clear I don't mean don't waste time on your clock (although that too), I mean don't waste your own time (correspondence games).

IM Silman's way with imbalances is an interesting approach.

Here is one of the many articles on it: http://www.chess.com/article/view/imbalances

Even if we say that time its not an issue, it's something that really depends from the position. The three stages of the game opening-middlegame-ending are at the same time one thing and separate. One static position can be change to a dynamic and the opposite were picking the right move it's something that affect or not that. Sometimes there are more than one good move to serve your plan but only one that promises more strategically. It's not always a simple procedure and that's why chess is not an easy game.

Basically experience makes the difference in the thinking process.

A GM doesn't think what moves should find, he already knows what he wants to play and why, so he's thinking process focus in details which the average chess player doesn't pay attention because can't recognize them.

I'm following the early moves along with several databases.  If I can find some video I'm watching that.  By the time we've left book (sometimes literally), I've watched a few dozen master game in the line and have at least a clue what typical plans are.  Now it's time to hit the analysis board and try to figure out some specific lines.  I copy and paste the lines in my notes and hope I've gone deep enough.  Usually by the time I make my move I have at least some plan, even if it's just "Oh I see what you're up to".  Sometimes I need a little sleep and fresh eyes to decide.  

Wow baddogno, you do all of that? I am sure that anybody doing that would improve with every game.

Here is my strategy for 30 minute games:

- Evaluate the position.

King safety? Material? Minor piece imbalances? Pawn structure? Best/worst pieces?

- Come up with a plan

Begin an attack? Pawn advance? Open or semi-open file? Go into an endgame?

- Evaluate the plan

What concrete moves will I play to excecute my vague plan? What can my opponent play? What will the result positions be?

- Evaluate candidate moves

Checks? Captures? Threats? What about moves which will help my plan come to fruition?

- Pick a candidate move

Which candidate move is best? 5 or 6 moves down the road, which position is best for me? Evaluate each position.

- Lose on time.

Oops, I used up my 30 minutes on move 5.

Here is my strategy for bullet games:

- See legal move.

- Play legal move.

When you only play one or two games, you have time.  Of course when you're old it's kind of a race between what you're learning, and what you're forgetting.  

Here is my simple method. Not foolproof, but it is a starting point: http://becomingachessmaster.com/2015/04/09/how-to-choose-a-chess-move/

My process is to just move whatever I want.