I'm a fifth year grad student, and I've taught several classes for freshmen and sophomores. This summer, as an "advanced" (whatever that means) grad student I got to teach an upper level class: Intro to Real Analysis.
Since this was essentially these student's first "real" math class, they haven't really learned how to study for or learn this type of thing. I've continually emphasized throughout the summer that they need to put in more work than just doing a few homework problems a week.
Getting a feel for the definitions and concepts involved takes time and effort of going through proofs of theorems and figuring out why things were needed. You need to build up an arsenal of examples so some general picture of the ideas are in your head.
Most importantly, in my opinion, is that you wallow in your confusion for a bit when struggling with problems. Spending time with your confusion and trying to pull yourself out of it (even if it doesn't work!) is a huge part of the learning process. Of course asking for help after a point is important too.
Question: What is a good way to convince students that spending time lost and confused is a reasonable thing and how do you actually motivate them to do it?
Anecdote: Despite trying all quarter to explain this in various ways, I would consistently have people come in to office hours who had barely touched the homework because "they were confused". But they hadn't tried anything. Then when I talk around an answer to try to get them to do certain key parts on their own or get them to understand the concept involved, they would get frustrated and ask "so does it converge or not?!"
It is incredibly hard to shake their firm belief that the answer is the important thing. Those that do get out of this belief seem to get stuck at writing down a correct proof is the important thing. None seem to make it to wanting to understand it as the important thing. (Probably a good community wiki question? Also, real-analysis might be an inappropriate tag, do what you will)