How to analyze your games

What is the proper way to analyze your games? Do you just go through to see what could have been done better and why, or what exactly do you look for and how as a lower level player do you know what to look for.

If you want the high level answer:

"Annotating a game takes 12-16 hours on average. For convenience, the whole task may be divided into 5 steps:

1. a) Play through the game quickly, taking 15-20 minutes, so as to call to mind again what you had thought and felt.
2. b) Go over the game in the course of an hour, and make a synopsis of its characteristic critical stages.
3. c) In the course of 3-4 hours, analyze the critical stages in detail.
4. d) Analyze the opening phase, taking care to fill any gaps in your knowledge of this variation. For this 3-4 hours are needed.
5. e) Go through the game and put together the commentary as a whole (4-5 hours).

Often, in the process of notating, you will convince yourself that your overall plan which did bring you a win in the game was nonetheless faulty. The fact should be self-critically disclosed, and not concealed in the undergrowth of inevitably specious analysis; theory and practice are united. The work finds its culmination in the conclusions about your typical, repeated errors - inadequacy of opening preparation, weak technique in endings, etc."

If you want the low level answer:

1.    Right after the game is over you should write down the thoughts you had in mind during the encounter. This will help you understand the nature of your mistakes later on. For example, put down: “I wanted to get the knight to f5, but was afraid of the move g5 by Black.” Or “I believed this exchange leads to a favorable pawn structure, so I wanted to trade all the pieces and win the endgame.”  At this stage there is no need for using chess engines. Of course, you may be forced to fix your openings if someone finds a hole there. Let your coach/second (if available) do it, or review the variation yourself, but don’t feed the whole game to your computer assistant.
2.    Once you have spare time (after the tournament), you should recall what happened over the board. Your notes will prove helpful at this point. Now you will have a chance to reconsider your decisions and try to understand where you went wrong. Try to scan the game move by move and find tactical refutations, positional errors, right plans, etc. Annotate the game again using a different color, e.g. “I wanted to get the knight to f5, but was afraid of the move g5 by Black”. "I guess I should have done that anyway since g5 runs into h4 with good attacking chances for White".
3.    After you’re done, you may finally bring your chess engine to the rescue. Take a look at the mistakes you have made otb and during your home analysis. Pay special attention to the positions where you couldn’t find the right solution after two attempts. For instance, if you blundered terribly otb, chances are you will be able to find the correct move at home. However, if the nature of your mistake was deeper, e.g. not understanding a certain middlegame position or not knowing how to handle an endgame, chances are you will face problems untangling it even during post-mortem.  In this case your PC or coach may prove extremely helpful.
4.    After you have reviewed the game and annotations using a chess engine, pay special attention to the key moments of the game. Memorize the associated principles, e.g. “in such rook endgames the pawns should be placed like this.” Or “in this opening the light-squared bishop shouldn’t be exchanged since keeping it is essential for protecting the light squares on the queenside.” Or “in such structures an isolated pawn may prove to be a force, not a weakness.” The same refers to your opening tree – make the appropriate changes.

I like IMBacon's so-called low level answer.  

Correct or not, i analyse my games by going through them the day after the tournament and make comment (annotate) on almost every move, how i was thinking when i made the move, and how i was thinking regarding my opponents moves. Then i switch the engine on to detect what i have missed. If possible, i love to get help from someone higher rated player to review the game with me and correct my way of thinking/evaluating a position. In total, a 2 - 4 hour work, depending on the game. This has helped me to detect my weaknesses so that i get a better understanding regarding which area i should put more efforts to improve.

Regardless of what someones rating is, its still a good idea to do your own analysis.  Sure its not going to be top notch analysis, and as you said they probably aren't going to find better moves.  But...what analyzing will do for them is it gives others an idea of what there thought process was, what they were thinking, what their game plan was, what their ideas were throughout the game.  Even with something as simple as: "Here...i didn't know what to do..." You can now give them ideas on what to do. 

Analysis isn't always about finding the better move/plan.  Sometimes its about asking questions, and getting answers. 

It's helpful for coaches if you analyze your games first.  Plus it's good when you review them a year later.  See how much you've gotten better. 

The reason a beginner should look at his games is not anything to do with chess theory.  Beginners make the same mistakes over and over, hang pieces, undefend squares and pieces, move onto unprotected squares.  It takes no knowledge of theory to do this seeing.  Till a beginner sees mistakes like these in his game and eliminates them, no study of theory will help.  Further, each player has his own weakness, and the weakness is in his own thought process, things that show up during a personal analysis of one's own games.

WHAT

I agree that it is helpful to review the game as soon as possible after the game was played.

i also agree that it is useful to analyze the game on your own, before turning to an engine. You can use the engine to answer specific questions, such as an error in the opening or a tactical miss. But self-analysis is going to be much more instructive than an engine.

one thing I do is try to identify a reason for a loss. Was the loss due to a tactical error? Opening mistake? Endgame error? Time pressure error? Basic lack of understanding of the position? And so on. This can help pinpoint areas to work on. I used this approach when I was playing tournament bridge, and it was extremely helpful.

i used to write down the time that I used for every move. (This is no longer allowed in some jurisdictions.) I found this useful to identify types of positions, openings. questions that I had trouble dealing with. This was very helpful.

i don’t agree that all of your games warrant this type of analysis. Some games are decided by a clear error and so you don’t have to look any further for answers about improving.