The thought process during game analysis changes somewhat as the player because higher rated and more experienced. The general analysis process is the same, but at the lower levels, the ideas must be found for the first time; whereas, for the higher levels, these ideas are mostly just recognized and heavily utilizing pattern recognition.
The goal of analysis (regardless of rating level) is to find improvements to the game moves. This usually means identifying suboptimal moves (especially blunders and mistakes) and figuring out why they are bad and what moves were better (and why).
I often hear that game analysis is important. But, what does that mean to you? How do you learn from your previous games? Is you object to not repeat mistakes? And if so, how do you achieve this?
I play a game. Step away for an hour or so, go back and run through just looking both sides moves. Then I go back later and set up a board. I play out each move, trying to find the best move and see if it matches my move. I also look at the recommended move and play that out. I just started doing this and hope that it helps.