You've already learned how to negate using the words "kein" and "nicht".
In German, there are other words to express negation:

Examples:
Ich verstehe nichts.
Ich bin nicht mehr deine Freundin.
Das hast du noch nie gemacht.
Nein, ich habe keine Bahncard.
 

"Nein" can be used to answer a question about decision. Its positive opposite is "ja".
"Nein" can stand on its own as an answer, but it is frequently followed by a comma and an explanation:

Example:
Haben Sie eine Bahncard? – Nein. Oder: Nein, ich habe keine Bahncard.
 

Qualifying the negation
Words like "noch" and "mehr" can be used to frame the time of a negation:

"noch nie" means that something has never happened up to this point in time.

Example:
Du bringst mir Blumen mit? Das hast du noch nie gemacht.
(= Harry has never previously brought flowers for Julia, but now he has brought her flowers.)

"nicht mehr" means that something was the case previously, but now is no longer true.

Example:
Ich bin nicht mehr deine Freundin.
(= Julia was Harry's girlfriend but now they are no longer a couple.)
 

Intensifying negation
The word "gar" can be used to intensify the negation.
It directly precedes the negation word.

Example:
Ich habe gar nichts gemacht. (I didn't do anything at all!)
Du willst mich gar nicht heiraten! (You don't really want to marry me!)