Using "だ" to indicate the state of things#
For example:
人だ
is a person
学生だ
is a student
Using "じゃない" to indicate the potential state of things#
In simple terms, it is the negative form.
For example:
人じゃない
is not a person
学生じゃない
is not a student
Using "だった" to indicate the past state#
Indicates what something was in the past.
For example:
学生だった
was a student
Using "じゃなかった" to indicate the past potential state#
Simply put, it is the negative form in the past.
For example:
学生じゃなかった。
was not a student.