Here are some tips for students, mainly focused on undergrads, but can be useful for the postgraduates too.

1. Keep a spirit/hunger for learning. Make use of every opportunity to learn from various resources, including teachers, books, friends, online resources, etc. and yourself.
2. Attend all the classes, even if you feel that the teacher does not teach well. Learning by yourself and learning from a teacher are completely different. Even if you learn from a very good book written by a very good author, that wouldn't be sufficient. Authors have many limitations, but your teachers may be free from such constraints. One example is that the authors can not give vague ideas; if they mention anything, they will have to include complete details in the book, and hence they usually do not attempt to do so. But your teachers wouldn't hesitate to do that, even if they do not know what they say in much detail!
3. Ask questions in the class. Do not feel shy or fear. If something is not clear, do not hesitate, raise the question. The question may turn out to be too silly or stupid; do not worry, keep asking. Slowly you will learn to ask good relevant questions.
4. Always discuss math with the other students in the class. Make it a habit, do it not only when you have doubts in the subject. Keep discussing topics, concepts, examples etc. with others. Even if you're the best in the class, be humble, and approach people for discussions; who knows if other people have better understanding than you. In fact, if you're the best in the class, then you have a responsibility to help your fellow students.
5. Whenever you learn a new concept, workout maximum number of examples and exercises as possible. One should learn math through examples; the modern way of learning math completely abstractly has many limitations, especially when you're not very mature in the subject. Every time you come across an example, try to discover better and more relevant examples by yourself.
6. As a continuation of the previous point, I should add that you may need to not only follow the teacher and the text book, but some further reading will be useful. You can make use of the internet/online resources for that. As a first step, I would recommend you to frequently visit the MathStackExchange and search for some interesting questions. Once you create an account, you can also ask questions, but very rarely you may need to, because a clever search in the website may show you that the question is already been asked by someone.
7. This is in connection with the previous three points. Never be happy with a single solution of a problem. If you get a solution to a problem, the problem may seem to be solved, but, look for more, you may find many different approaches to the same problem. For example, in MathStackExchange, you will notice that only one answer may be selected as 'the answer', but the other answers and comments will also be very important.
8. Learn how to write math. Keep an eye on the way the teacher writes proofs or other mathematical statements, practice yourself, be careful with mathematical writing even while making personal notes or while writing exams and other assignments.
9. Don't choose a particular subject as your favorite. Students usually have this tendency to choose either one or two of Analysis, Algebra, Topology, Applied Math etc. as their favorite, and start avoiding the other subjects; this is not healthy. I would recommend a postgraduate student to do that, but only after the first year. An undergrad student should learn, without any partiality, each and every subject taught in the course. In future you may end-up doing research in a particular area of Mathematics, still the techniques learned from other courses would help you.
10. Try to attend workshops/summer schools during your semester breaks. The MTTS programme is a very good choice, but, keep in mind that you may not easily get selected, because, the organizers receive a large number of applications every year, and they wouldn't be able to accommodate many students. If you're lucky, you may get selected, so apply without fail. Sometimes, colleges located in your neighborhood may organize public talks or short-term workshops for undergrad students; attend whenever possible.
11. The teenagers, being revolutionary by nature, will feel at some point during their undergrad course that these exams and marks does not matter; what matters is how well you understand the subject. That is correct, to some extent. But you will have to score not very badly, so that you may not be stopped on your way to higher education or other heights.
12. Keep a healthy competitive mind, do not aim for being better than rest of your class, but aim for being one among the best students. As already mentioned in the 4th point above, once you become one among the best students, you have a responsibility to help the weaker students to come up to your level. Some of the students may have difficulty in understanding new concepts discussed in the class, and a teacher may easily figure it out; so, in case if you feel that the teacher is unnecessarily giving repeated explanations, do not interfere, be patient, and let the teacher confirm himself/herself that all the students have understood well.
13. Be active in group discussions, and utilize every opportunity that you may get to improve your teaching/presentation/leadership skills.
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