"My sister never drinks."
Translation:Η αδελφή μου ποτέ δεν πίνει.
It may make more sense if you think of ποτέ as "ever".
Τον έχεις ποτέ δει; "Have you ever seen him?"
So it needs a δεν to make "not + ever = never". Ποτέ δεν τον έχω δει "I have not ever seen him = I have never seen him".
Similarly with some other words such as κανείς -- which by itself means "someone" and needs a negative to make "anyone" out of it.
Κανείς έφαγε το ψωμί μου! "Someone ate my bread!"
Κανείς δεν τρώει το ψωμί του. "Nobody (= not anybody) is eating their bread."