There are a lot of chess improvement plans floating around the internet. I'm going to present one more, slowly, over time. The focus of the plan is on improving a player's OTB game, and in my view there are four elements requiring some level of study: (1) tactics, with an emphasis on visualization and calculation, (2) position evaluation, (3) strategic understanding, and (4) memorization, particularly openings and endgames.
I believe that every chess position is a puzzle to be solved and thus general rules should be of theoretically limited importance. Having said that, the majority of chess positions are "quiet" and solving a puzzle with no clear objective solution will invariably require some shorthand (or, yes, general rules). I'll also concede that the lines may be blurred between and among the above categories and that I may not have them listed correctly, or at least, in the best way. For example, the lines between (1), (2), and (3) above seem vague and there will be overlap between the ideas. I think this is true because there will be some level of aritificiality and arbitrariness to any way in which you attempt to sub-divide the game. For example, to master the game one needs to have a grasp of minority attacks and play against or with the isolated queen's pawn. I would place these concepts into the category of strategy (3), but they'll also obviously be a large part of evaluating a position (2). In the end, I'll leave it to others to describe the proper elements of chess study, and to ascribe their importance, and I'll get on with aiming my discussion at calculation and visualization (including especially tactics), strategy, and memorization/understanding (including as a big part, opening and endgame study). I'll use blog labels for posts related to this subject of "chess improvement," "tactics," "visualization," "calculation," "position evaluation," "strategy," "opening study" (as opposed to "opening theory"), and "endgames."
This exercise is as much about improving my own game as it is in sharing my thoughts about how to become better. I'm trusting that sharing the plan here will be an impetus for thinking more carefully about the subject. I have limited OTB experience, and in fact, my biggest hurdle may be finding time to test my progress (playing OTB). I'm almost entirely a correspondence player and correspondence chess deemphasizes especially visualization making it a somewhat different game. The goal is nevertheless to get objectively better at a reasonable pace. The exercise seems healthy to me, even if it's only done for self.
Finally, a word about de la Mazza's Rapid Chess Improvement. The book invariably comes up on the subject of chess improvement for adults. Please note that it's almost entirely a plan to improve your chess tactics. In short, I think if you follow it, you'll be rewarded. All of my instincts, however, tell me to take a more balanced approach, even though tactics occupies a special place in chess improvement.