This question was forwarded to me recently by a budding keen and serious player so let the following be a guide:
Best Answer - Chosen by Asker of Yahoo Answers.
The best way to improve is to have a coach or study and play regularly.
Although focusing on your weaknesses always yields the best returns, all class players benefit greatly from:
1. Play serious (read tournament) games often. (Review them and learn from them, even wins can contain many mistakes) This also means avoiding rapid online games where you're actually practicing your mistakes.
2. Solve tactical puzzles.
3. Study the endgame.
Openings are near the bottom of the list. Fix any major problems but don't sit around and memorize variations -- the += you get out of all your work will be lost in the next few moves (once you're out of book) unless you're master strength.
You got good advice where Silman's reassess book was recommended. I got the book when I was 1400s and I still find the material good as a class A player. It's famous for making GM type positional thinking accessible to class players, you cant go wrong with it. If only for his idea of imbalances and how to come up with a plan. An imbalance, according to Silman's books, is any difference in position between the two sides. After recognizing the differences you work to strengthen your pluses, reduce your weaknesses and vice-versa to your opponents position. In the opening you will suddenly be learning what imbalances you're working toward creating. Although it doesn't really fit into one of the categories I listed above I'm going on about it because it's a very good book and I recommend it :)
For tactics I recommend "Sharpen Your Tactics" I also enjoyed "The Ultimate Chess Puzzle Book" because it's tests didn't seem to be the standard, I see the idea so I know it works, type of puzzle. You may find the correct first move, but if you failed to find the best defense you realize the continuation you planned on playing would have lost in a real game.
For the Endgame, Silman's Complete Endgame Course (a book) is regarded well. He divides endgame knowledge into each class level giving the reader only what they need to know based on their current skill. He is very good at making what is usually dry boring endgame material enjoyable and easy to absorb. I must recommend also Dvoretsky's Endgame Manual which is highly regarded, also I enjoyed working through it.
By studying regularly you'll see improvement. Usually players will hit a plateau where it seems like they aren't improving, then suddenly they'll "jump" to the next level. Good luck :)
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