Pieces of advice:
Theory building: A student must have or acquire a working knowledge of Discrete Mathematics, Algorithms, Theory of Computation, Probability Theory, Linear Algebra, Modern Algebra, Metric Space Topology and Real Analysis, Combinatorics, Graph Theory, Algorithms for polynomials and numbers, Complexity theory, etc kind of theoretical subjects. Read standard textbooks, e.g. Topics in Algebra by IN Herestein, Topology of Metric Spaces by S. Kumaresan, Mathematical Analysis by Walter Rudin, Introduction to Automata Theory Languages and Computation by Hopcraft and Ullman, Algorithms by Coreman Rivest et.al. etc., and listen to standard video lectures like videos from NPTEL, Coursera, eDx etc.
Problem-solving skills: Parallel to theory building develop problem-solving skills. First, solve easy problems (textbook kind) and then try harder and harder non-routine problems. This skill is hard to acquire and nobody can teach you. The good books for this purpose are a series of Titu Andresscu books on number theory and combinatorics (no need to do algebra and geometry because it is not part of the CS discrete mathematics syllabus), and Problem-Solving Strategies by Arthur Engel. Also, you cannot create a good problem until you are not a good problem solver. To publish the research work in good venues we have to solve a good quality problem.
Reading papers from top venues like; Conferences: FOCS, STOC, ICALP, MFCS, FST&TCS, etc. Journals: SIAM Journal of Discrete Mathematics, SIAM Journal of Computing, IEEE Transaction on Information Theory, Combinatorics Probability Computing, Random Structure and Algorithms, Combinatorica, Combinatorial Theory Series A and B, etc will increase the understanding of the students. Solving their problems will not be possible but these papers can be read.
The students must read papers from peer-reviewed venues and must submit their work to peer-reviewed venues.