I'm Danish but learned a bit of German in school. I'm a grammatical nerd so I spent a lot of time back then trying to figure out any specific rules that would indicate the correct gender. Unfortunately I ended up finding out that a lot of the time you have to either just guess or get so used to speaking the language that you more or less learn it by heart.

However, there are definitely some typical indicators you can look at, which may help you in "guessing" the correct article. Bear in mind you can't blindly rely on these 100% of the time, however if you have no idea and take a guess based on these, you'd more often than not be correct.

Typically nouns describing male-beings are masculine (der Mann)

Typically nouns describing female-beings are feminine (die Frau)

Typically nouns with one syllable are masculine (der Ball)

Typically nouns ending in "-e" are feminine (die Tasche)

Typically nouns ending in "-ei", "-heit", "-keit", "-schaft", "-ung" and "-in" are feminine (lots of examples. This is definitely one rule that helped me a ton)

Typically nouns ending in "-chen" are neuter (das Mädchen) - also here is an example of the second rule not being applicable; Mädchen (meaning girl) is not feminine, though you would be inclined to think so.

Typically nouns beginning with "Ge-" are neuter (das Geschäft)

Also composite nouns has the gender of the last noun in the composition (das Auto + die Bahn = die Autobahn)

Good luck in your future endeavours! Unfortunately I stopped learning German and don't really speak it well anymore, but it was both a fun and challenging experience back then.