Looking at any training program, one must consider the performance objective and how to train the component parts that go into it. For chessplayers, the primary long-term objective is to increase your playing strength to improve game performance; put more simply, to win more often and against stronger opponents. While it's not completely cut-and-dried, chess can usefully be broken down into opening, middlegame and endgame phases, with different principles and techniques that dominate in each. To use a sports analogy (as in "Chess vs. Tennis - sporting lessons"), if one is training to be a better tennis player, the primary objective (win more and against better opponents) is exactly the same, while the game can be broken down into elements such as your service game, return game, baseline play, net play and shot selection. Other sports analogies can be used as well, for example long-distance running. That is an excellent illustration of the fact that while it's important to train a variety of things, the main focus needs to be on actually doing the activity you are training for; runners can do other types of physical and mental training, but in the end the best training for running is, in fact, running. (My view of chess training is broadly similar, as reflected in "Analyzing your own games is more than just analyzing your own games".)
I use the sporting analogy because it may help highlight the idea, in a more intuitive way, that chess performance in the end is a combination and culmination of many different things - training of component skills, application and integration of those skills in a "real-world" environment, judgment, mental toughness and creativity. Perhaps it's because so much goes into a chess game or tournament that our egos often become involved and if we're not careful, it can seem like our personal worth is on the line with the result. The same thing happens in sports - I consider chess to be a mental, individual sport - as athletes have good days and bad days in team matches, or in an individual sport get crushed in one tournament but then find the mental fortitude to do well in the next one.
So how does this broader perspective factor into the question of study techniques in chess? I think improving players can often lose sight of the goal, namely improving playing strength and performance in actual games, while focusing on training component parts. This is most obvious with tactics drills, where it is easy to keep solving problem after problem and honing your ability to find 1001 mating solutions in the quickest way possible, then fail to find the way forward in over-the-board situations where mating attacks are nowhere to be found. While the description is somewhat exaggerated, this is in fact a common trap.
Does this mean that tactics drills are useless to improve your performance, as are other specific study techniques for openings, middlegames and endgames? Of course not. I used to be quite weak on tactics (believing myself to be a "positional" player - the subject of "Playing Styles Deconstructed" - and therefore not needing to dirty my hands with it). Once I realized the folly of this, I greatly improved my tactical understanding and performance by studying Understanding Chess Tactics and applying myself on the Chess Tactics Server and the Chess.com tactics trainer. I do believe, however, that any training program that fails to take a holistic approach to chess and instead focuses only on training a single component skill will ultimately fail. Also, your training program must be realistic and calibrated to your current level of understanding - pushing the envelope, as mentioned in "Mindfulness and Effortful Study", but not ripping it to shreds.
Finally, an important consideration when determining how you should study, as compared to generally what should you study, is your learning style. Learning styles vary greatly and I think this fact is underappreciated in the chess improvement community. Some common training principles are worth emphasizing, as I did in the tournament chess skills post, but especially at the amateur level I'm a big believer in the "whatever works" school of training. This is because it's done as a pastime, for love of the game, so the motivational factor is so important; if you hate a training method, you're simply not going to want to do it any more, regardless of how effective it is supposed to be (according to Authority X). If you don't believe this is important, simply search through the chess improvement blogosphere, which is littered with dead "Seven Circles (of Hell)" blogs.