There is a good deal of scientific and even philosophical debate about chess training. I tend to think there is an over-emphasis on trying to find a single, objectively best path for improving chess skill. I honestly doubt such a beast exists, actually. Certain components are going to be common to any chess training program: opening study (including ideas of the opening and resulting middlegame formations); tactical themes and practice; how to strategically evaluate positions in the absence of winning tactics; and endgames (especially how to reach key endgame positions that win/draw by force).
Exactly how one goes about studying each of these areas I assess is not as important as the fact that one is, in fact, dedicated to studying them, in some type of regular and systematic fashion. Some people's minds work best with a great deal of organization and structure; others reject that in favor of more intuitive or loosely-organized arrangements. Personally, I work best somewhere in the middle. The point is, work (even if it is pleasurable work in hobby form) needs to be applied consistently over time.
From my observations, successful training occurs when a person is mentally committed to achieving a goal; understands at least in a broad sense what will be involved; and has the time and energy to maintain a regular training schedule. The first point is more or less self-explanatory. The second point is, I think, where many people can go off the track willfully or no, for example searching for "the way" to most quickly improve. And mis-assessing the third point is a major reason for people having to abandon overly ambitious training programs.
I consider all of the above to be interrelated, although it's useful to break down training components to see if one is lacking in what is necessary. Half-hearted commitment is worse than nothing, since it leads to wasted time on something you didn't really want in the first place. A willingness to study material from various sources, think critically for yourself, and have a broad mind are all key to learning effectively. Finally, we all have life constraints and trade-offs that require us to set realistic goals, if we wish to achieve them.
A word on cross-training I think is useful in this context. Similarly to what occurs with cross-training in physical pursuits, mental cross-training does appear to have positive results. My personal experience with training Taijiquan (Tai Chi Chuan), which has both mental and physical components, has given me a much better capacity to focus and have a clear mind during chess games. Independently, I've seen more than one master-level player comment on this phenomenon - Josh Waitzkin being perhaps the most famous one - so it's apparently not just me.
To sum up, I believe that whatever methods work best for an individual should be how that person pursues a training program, since it is they who will be finding the motivation, searching for substantive knowledge, and setting aside time to in fact pursue it. It is useless to follow training methods which work for others and even which may be objectively best, if they are in your case demotivating and unhelpful. I find there is a major parallel with physical training programs, in that it is much more productive in the end to do a useful physical activity that you enjoy (walking, swimming, etc.) 3-4 times a week than to randomly try workout programs and then abandon them.