Read this excellent article on how to improve in chess.
I think I may have a slightly different take on the topic once I get to master, but that is better than I could write right now.
One thing I would change is not to use a problems book. I would concentrate on web resources like Chesstempo.com and Shredder's problems. The only problem book I recommend is Ray Cheng's Practical Chess Exercises.
I would add that you should study your own tournament games, and make flash cards of game and problem errors you can generalize into a lesson.
I want to re-emphasize this: lots of Experts and Masters do not play book lines. Memorizing opening lines is a waste of time, but studying annotated games in the openings you play is good. GM Christiansen's advice to play over lots of GM games (unannotated) in the openings you play may be good, too. You want to learn common tactics and strategies for the openings you play, and understand the why of moves, not memorize move sequences. Seirawan's Winning Chess Openings is all you need for quite a while.
Update: An email from a friend prompted the following distillation:
My current thought is that great improvement can be had for 1000-1800 level players by focusing on three areas: tactics, playing discipline, and understanding the game.
Understanding the game, starts with the endgame. It is easier to grasp the strategic elements in an endgame, when there are fewer pieces on the board. Playing over well annotated games in your openings is another piece. Analyzing your own games and trying to develop general lessons from your mistakes is the third piece.
Playing discipline encompasses having and following a move method (including blunder check!), clock discipline, and a good attitude.
I think tactics can be addressed by a general overview and then lots of puzzles.
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