Noun, neuter
You now know that Coming-out is neuter. But what about all the other German words? Do you have to learn the article of every single word by heart?
Unfortunately, German has only a few general rules that help you work out a noun's article. Grammatical gender in German is often not intuitive at all, and a thing's natural gender rarely helps. Girls, for example, are naturally female, yet the word “Mädchen” is neuter: you say “das Mädchen”.
So if you want to be sure of a word's gender, you have to learn it by heart.
Luckily, German does have a few gender rules that make things a bit easier. Of course it would be even better if those rules had no exceptions – but you can't have everything!
Colours – such as “das Gelb” or “das Rosa” – are almost always neuter. So are nouns ending in -chen / -tum / -ment: das Märchen, das Stadium, das Testament.
Many words to do with time and dates – der Mittwoch, der August, der Winter – are masculine. Many weather nouns are masculine too: der Wind, der Regen, der Hagel. Most alcoholic drinks (except “das Bier”!) take “der”: der Schnaps, der Champagner, der Gin. Words ending in -ig / -ling / -ich / -en are almost always masculine as well, for example der Bahnsteig, der Wüstling, der Rettich and der Hafen.
Almost all kinds of fruit (apart from a few such as “der Apfel” or “der Pfirsich”) are feminine. Many suffixes also appear almost only on feminine words: -in / -heit / -schaft / -ei / -keit / -ung / -ion, as in die Rektorin, die Anwesenheit, die Belegschaft, die Fischerei, die Einsamkeit, die Zeitung, die Adaption.
If you know a noun's gender, you also know its indefinite article. German has only two: ein and eine. Feminine nouns take “eine”; everything else takes “ein”. So it is ein Coming-out.
You use an indefinite article when you are not quite sure (or don't need to be) exactly who or what you are talking about.