So, some things that I've been trying to get at these "student skills":
1) Journal prompts asking students to reflect on how well they feel like they're doing with the current lesson, what questions they have, and how they're going to address their questions.
2) More journal prompts asking students to reflect more broadly on how they're studying and keeping themselves engaged during class.
3) One-on-one meetings with students where we set individual goals and talk about progress in meeting them. (I haven't done these as much as I'd like this year... this is a good reminder to start these back up.)
4) Emphasizing over and over again the importance of effort, perseverance, and asking questions and that this is what's under their control and should be the goal towards which they're working rather than an abstract "I want to get a good grade."
5) Distinguishing between general effort and reflective and directed effort... for example, homework credit is only given for assignments in which the answers have been checked and mistakes have been corrected (with ample opportunity and encouragement to ask questions in class), not just for attempting problems. Part of students' participation grade (10% of their overall grade for my more-struggling classes) is predicated on asking thoughtful questions.
6) Focusing my comments on grade reports on progress made and effort expended and not just on results reached.
I'd love to hear of ways that others encourage students to push themselves and become better learners.
Some journal prompts: