Start with requirements gathering and analysis with the users to find out, among other things,
1. Who and What are involved: Teacher, Student, Subject, etc => Entities
2. What are their relationships: e.g. every teacher can teach multiple subject, every teacher can teacher many students, etc => Relationship
3. What data do they capture, any system, documents (forms, letters) they use to do this job currently? => Reveal data attributes and existing work flow.
4. What are other other requirements.
It is impossible to explain the design of a database here, you may refer to Introduction to database design
]. It is a matter of trials and errors, but you get better with more practice. Always go through your design with the users until they are satisfied.