There are some rules ... and more exceptions (again: some are already mentioned above)
rule "der"
"e" at the end of the word and the German Umlaut on the vowel.
der Baum - die Bäume
der Schrank - die Schränke
exception:
a noun is ending on -el, -en, -er => no change at all
der Esel - die Esel
der Hamster - die Hamster
das Mädchen - die Mädchen
exception: der Apfel - die Äpfel, der Bruder - die Brüder, der Laden - die Läden, der Vater - die Väter
and some more exceptions ......
rule "die"
noun in plural comes with "en" (except noun is ending on "r" or there already is en "e" at the end)
die Frau - die Frauen, die Katze - die Katzen
die Dame - die Damen
die Schwester - die Schwestern
nouns ending on -nis: +se
die Erkenntnis - die Erkenntnisse
rule "das"
no change in plural with nouns ending on -el, -en, -er, -chen, -lein
general guideline: nouns ending on a vowel, add an 's'
das Radio - die Radios
das Kino - die Kinos