In German, nouns have three grammatical genders: masculine, feminine, and neuter.
From what we've heard from our German-learning friends, language courses simply get away by saying "You need to memorise every word with their articles, there is no other way". That is not how languages work...
Masculine Nouns
Nouns referring to male individuals or animals.
Seasons, months, days of the week, and compass points.
Most nouns related to things that perform actions.
Nouns ending in -ich, -ig or -ling.
Nouns borrowed from other languages, ending in -ant, -ast, -ismus or -or.
Feminine Nouns
Most nouns ending in -e. (Note: Male individuals or animals ending in -e are still masculine, the "Ge- -e combo is neuter.)
Nouns ending in -heit, -kwit, -schaft, -ung or -ei.
Counting numbers.
Nouns borrowed from other languages, ending in -anz, -enz, -ie, -ik, -ion, -tät or -ur.
Neuter Nouns
Most nouns beginning with Ge-.
Nouns ending in -lein or -chen.
Expressions related to fractions.
Nouns referring to the young humans and animals.
Infinitive verbs used as nouns.
Nouns ending in -nis, -tum.
Nouns borrowed from other languages, ending in -at, -ett, -fon, -ma, -ment or -um.
Remember that these guidelines are a framework, exceptions always exist.