Studying and teaching chess is not a very exact science. There seems to be no hard and fast rules as to what to study, how much to study, how to study, when to study, ratio of study to practice, and even goal setting to direct study. Everyone seems to have their own way, which reflects in the fact that there is no universal style to chess.
Some players devour opening theory, which can help with tactical knowledge and plan creation in complicated positions, but usually does little to help with technical play. Studying openings can also lead to psychological weaknesses, as gaps in opening knowledge become apparent and worried about, while reactions to non theoretical moves can be poor.
Some players solve thousands of tactical exercises, which can help with their pattern recognition. While tactical vision is a key element of a successful chess player, it is only one factor, and a danger in working solely on tactics can be a reliance on them, and a need to make certain tactics work in positions where they may not be justified.
Some players study endgames (I might be guilty of this), following in the footsteps of Capablanca. This study of simpler positions and technical precision can help a player earlier in the game to understand weaknesses, relative piece strengths and the transition to the endgame stage. But exclusive endgame training can dull creative and tactical vision, and lead players to search for simple solutions in the middlegame, where a may forceful, or dynamic approach may be necessary.
Of course, the best answer is to mix up that which is studied. Try to solve some tactical puzzles regularly, keep working on openings that you play, or that interest you, and look at theoretical and technical endgames. How much a player studies will depend on that player's time commitments. A working adult, who is very keen on improving might be able to devote 5-10 hours a week on chess study, but then again, they might only be able to put in an hour a week, especially if they have family commitments. So what should these precious hours be spent on?
Playing chess is of paramount importance, and studying your own games is the next most important things. Being extremely self critical in your analysis is key, and analysing without a computer is important as you then simulate analysis that will be used in a game. Checking your analysis with an engine is fine. Much of the opening work you undertake can come from post mortem analysis, when you check to see how your play in the opening went, and then look to improve your knowledge of that opening. If you prepare for games, then some opening analysis will also happen. But beyond this what should you do?
I read an interview with American women's super star, Jennifer Shahade, where she was asked this question. She suggested that 40% of your time should be spent on the middlegame, 30% on the opening, and 30% on the endgame, at least for non master players. I found this interesting as so many Grand Masters have suggested opening study as relatively unimportant compared to tactical study or endgame thinking, and this balanced approach seems to make more sense to me, especially as some players find certain elements of the game more interesting. I would also add that players who are self studying should be happy with whatever they are doing, as any study is better than none. So if a player loves attacking chess, then I see nothing wrong with them looking at lots of classic games with elegant mates, and solving tactical puzzles. At some stage they should find out that a one sided attacking game alone will not suffice at a certain level, and they can then feel the need to study other parts of the game.
In my opinion, the best way to study a balanced, all round game is to look at annotated games. These will probably give some basic thoughts to the openings played, will examine the thinking processes of the players, especially if the author is playing, and will consider both tactical and technical aspects of the game. A good book of a games collection is invaluable in any players library, and should be worked through deeply, and critically. The ideas and general advice that can be gained is invaluable and can lead on to other areas of study. Seeing a great player handle an opening that we don't know too well can inspire us to explore that opening. Likewise, finding analysis of classic endgames can engage us in that subject and make us inquire more deeply about certain types of technical position.
So I intend to post classic games here from the books in my collection, which isn't extensive, but still has quite a number of titles. I'll try to post a game per day, though there might be times that I'm too busy for this. In the meantime, I'd be interested to hear form both payers and coaches how they feel players should study the game.