I don't really analyze GM games unless they are model games for openings I am trying to play or something.
I do analyze my own games.
Recently, I started using an analysis process which is very long and time-consuming, but gives me great analysis and no doubt helps me with my chess. It does use computers, but not until the end, and until then, you get great training by doing your own analysis.
First, you write down all the thoughts you remember having had during the game and when. Also make note of the time on the clock at all the key points.
Then, you use a large database to look up the opening in the game and continue all the way through, exploring every variation, until your game goes out of book. The point here is to see whether or not you played perfectly, and whether or not you plan to use those same moves again if the opponent plays the same way. Additionally, you can see whether your opponent played the best moves. This part usually takes a good two hours or so if you are really doing it correctly.
The next part, and the hard part, is the Dry Analysis, as I like to call it. Basically, you go from the position that your game went out of book, and then challenge yourself to find the best move on every turn for both players for the rest of the game. Examine and write down your thoughts for all notable variations and try to annotate the game, assigning evaluations and exclamation points or question marks on the moves that deserve them. For a complicated game, this part has the potential to take more than three hours.
The last part is the Engine Analysis. This is where you check over your Dry Analysis to see what you got right and what you didn't. The engine may, in the case of one of my most recent games, spot a hard-to-see tactic that you wouldn't have seen during Dry Analysis, or provide more accurate evaluations. This part should take about an hour. It's important to do engine analysis last because doing it early on is like looking at the answers to a test- you get the answers but you don't build the relevant muscles by doing the Dry Analysis.
Of course at the end you can put it all together into a completed game analysis and publish it or show strong players and see what they think. The whole process should take at least five or six hours total.
It may be applicable to a GM game. You can still go through the opening to see where it went out of book, you can still do Dry Analysis, and you can still do Engine Analysis. But until you get to at least a high class level in your rating, analyzing games of GMs won't do you much good. GMs are so subtle in their play and so perfect in their moves that you won't learn much- they don't normally make mistakes that are instructive to normal players.
Somebody explained to me lately that spending 30 mins going through a gm game won't teach you anything (not sure if that's a gold rule of chess or just applies to beginners like me)
So for the last 2 days I've taken it REAL slow. I'm analyzing one of the most famous games, Paul Morphys 1858 game, against count Isouard\Duke karl. The problem is, I can make general speculations in notable areas of the game (say... when Morphy sacs his knight for the nice bishop pin setup). But for the life of me when I flip the board and try to find how black could of stopped morphy, I fail badly. It's like a bias I can't shake off.
All I could get out of this game was:
*don't favor weak attacks over controling the center (not that I could identify a 'weak attack'.)
*Don't play an opening you know nothing about (wow no kidding dummy!)
*White gained an advtange because black gave white an oppertunity to bring the queen out early without danger.
*Black should of played 9.Na6, putting pressure on whites queen, and forcing white to consider exchanging the bishop for knight. (I think this is the only good thing I learned, but only because a little birdy named fritz suggested it to me).
So what would be your suggestion for proper analysis? And is the points I made about this particular game correct or unhelpful? Thank you chessfriends!