Similar to Kramnik's commentary in "How Kramnik makes us feel better about chess", I found Carlsen's approach to chess and his views on playing and training to be refreshing, having a simplicity and mature clarity about them. When top players matter-of-factly discuss how positions are unclear and admit their own limits, it's an important lesson for improving players as well.
The article is worth reading in its entirety, but I've excerpted some of what I consider the most relevant points on mental attitudes, the importance of developing intuition and the role of planning.
- "...what at first seems like studied indifference is a genuine character trait of not easily becoming worked up, of taking things in one’s stride rather than needing to feel always in control. In fact, Carlsen seems unfazed by many things, among them not knowing whom he is playing when, how well he has to do in the London Classic to beat Kasparov’s record, or, for that matter, where to meet for lunch."
- "...Carlsen says the difficulty with being tired when playing chess is that things don’t come intuitively. I point out that the stereotypical image of the game is that it is won not through intuition but hyperrational analytical powers. 'Of course, analysis can sometimes give more accurate results than intuition but usually it’s just a lot of work. I normally do what my intuition tells me to do. Most of the time spent thinking is just to double-check.'"
- "Still intrigued by the claim that intuition has pride of place, I ask him about the importance of spontaneity in chess. 'Of course, you make plans but the positions are often too complicated for proper planning. Then suddenly you get an idea.'"
Carlsen also emphasized the importance of being able to feel the joy in chess, rather than having it become a grind. This and all of the above points I think are quite applicable to the improving player.