Since you don’t want textbook definitions, loosely speaking, a super key is a set of columns that uniquely defines a row.
This set can have one or more elements, and there can be more than one super key for a table. You usually do this through functional dependencies.
In your example, I’m assuming:
StudentNumber unique
FamilyName not unique
Degree not unique
Major not unique
Grade not unique
PhoneNumber not unique
In this case, a superkey is any combination that contains the student number.
So the following are superkeys
StudentNumber
StudentNumber, FamilyName
StudentNumber, FamilyName, Degree
StudentNumber, FamilyName, Degree, Major
StudentNumber, FamilyName, Degree, Major, Grade
StudentNumber, FamilyName, Degree, Major, Grade, PhoneNumber
StudentNumber, Degree
StudentNumber, Degree, Major
StudentNumber, Degree, Major, Grade
StudentNumber, Degree, Major, Grade, PhoneNumber
StudentNumber, Major
StudentNumber, Major, Grade
StudentNumber, Major, Grade, PhoneNumber
StudentNumber, Grade
StudentNumber, Grade, PhoneNumber
StudentNumber, PhoneNumber
Now assume, if PhoneNumber is unique (who shares phones these days), then the following are also superkeys (in addition to what I’ve listed above).
PhoneNumber
PhoneNumber, Grade,
PhoneNumber, Major, Grade
PhoneNumber, Degree, Major, Grade
PhoneNumber, FamilyName, Degree, Major, Grade
PhoneNumber, Major
PhoneNumber, Degree, Major
PhoneNumber, FamilyName, Degree, Major
PhoneNumber, StudentNumber, FamilyName, Degree, Major
PhoneNumber, Degree
PhoneNumber, FamilyName, Degree
PhoneNumber, StudentNumber, FamilyName, Degree
PhoneNumber, FamilyName
PhoneNumber, StudentNumber, FamilyName
A candidate key is simply the “shortest” superkey. Going back to the 1st list of superkeys (i.e. phone number isn’t unique), the shortest superkey is StudentNumber.
The primary key is usually just the candidate key.