How would i do this?

I am new to DB programming, so im not too sure about how to implement my DB.

Here is what i need: a DB with tables of:

1. Students.
2. Classes
3. Teachers
4. Assignments

Each teacher can be assigned a class, which is compromised of a list of
students. Each class can be given assignments.

Coming from a programming background, I could do this in c++ very easily. I
actually started inmplementing it in a similar fasion: each student class
teacher ect would have a uniqe id in the database, and, for example, a
class would include an array of integer student id's.

This seems really error prone, and not very efficient.

what is a better implementation?

John Hughes