Does "den", "dem", and "des" also mean "The" (like along with Der, die, and das) and if they do, how do you know when to use them, and if you don't what do they mean?

Question

Ema_non · Answer

Yes, "den", "dem", "des" etc. all mean "the". They are used depending on their function in a sentence (case), their grammatical gender and quantity (singular, plural). A system with a declension and case system like that has the advantage that the sentence structure can be more fluid than e.g. English, because you can recognize the function of the noun through the case/declension. For example you can put an object right at the beginning of a sentence in German, which would sound strange in English. 
Declension tables (the proper endings) have to be memorized.

This sentence e.g. starts with an object in the first position:
- Den Mann da drüben habe ich noch nie zuvor gesehen. (I have never seen this man over there before)

In the following sentence "der Mann" in the first position makes it clear that it is the subject of the sentence:
- Der Mann da drüben hat gestern mit mir gesprochen. (The man over there talked to me yesterday)

Ema_non · Answer

@miniaturemagi 
If you take a look at the declension table which carmii posted, you can find "den" in two spots:
- Akkusativ Singular Maskulinum
- Dativ Plural

"Akkusativ" in general denotes a case where a person or an object is directly acted upon. "Dativ" in general denotes a case where a person or an object "receives" something.

- Ich gebe ihr den Stift. (I give her the pen)
In this example, "her" would be in the dative case because she receives something.
"The pen" is used with the accusative case, because it is the object that is given (acted upon).

So if you know what a noun is supposed to do in a sentence you can apply the correct case (and thus the correct article)

I recommend reading this page here: https://germanwithlaura.com/noun-cases/
It's a bit lengthy, but after that you will have a better understanding of how the German case system works.

Ema_non · Answer

@Iambob You're welcome. "Thank you" means "danke" :)

what_ohno · Answer

Yes it all means "the" and the difference is the grammatical case, which is one of the fundamental concepts in German that learners of the language have to struggle with.

There are 4 cases in German, which are Nominativ, Genitiv, Dativ and Akkusativ. You know genitive from English too, while Akkusativ and Dative are similar to the concepts of "direct object" and "indirect object" in English.

For instance, in the sentence:

The boss introduces the new caretaker to the team.

The three "the" need to be translated into "Der" (Nominativ for the subject), "den" (Akkusativ / direct object), "dem" (Dativ / indirect object).

German has a lot more inflection than English. English has plural and tenses, but German also has gender and cases.

what_ohno · Answer

@Iambob Unfortunately the only true answer is that whenever you learn a verb (or preposition) in German, you also have to learn the case that the objects need to have. So when you learn "geben" (to give), you learn about one object in accusative and one in dative. Like @Ema_non said, there are some general rules that can give you an idea of what might make sense in many cases (no pun intended), but for some verbs you just have to know what is right (like in the other example, "das Auto gefällt dem Jungen", the boy likes the car and the boy is dative, it does not really make sense so much).

Actually there are similar things in most languages. In English we learn how to say "I look forward to seeing you tomorrow". Why is there a "to" and why do you need to use "seeing" instead of "see"? What is the difference between "I stop eating" and "I stop to eat"? (Or "I like eating" and "I like to eat"?) There might be some general rules, but in essence we just have to learn it by heart when we learn English. When you learn the words "stop" or "look forward", you also have to learn how to put the objects into the sentence.

what_ohno · Answer

@Iambob Don't be discouraged. With a good teacher and/or study methods, I'm sure that after a while you'll get a different perspective on the things that seemed hard or impossible to learn at first. It was the same for me with Chinese, which also has the reputation of being difficult to learn.

carmii · Answer

You have to learn the concept of the German cases and grammatical genders first.

The nominative is used to show the subject.
The genitive is used to show a possession.
The dative is used for indirect objects.
The accusative is used for direct objects.

This concept doesn't exist in the English language.

Das Auto gefällt dem Jungen.
Das Auto: subject (neutral)
Dem Jungen: object (masculine, dative)

Does "den", "dem", and "des" also mean "The" (like along with Der, die, and das) and if they do, how do you know when to use them, and if you don't what do they mean? See a translation

@Iambob You're welcome. "Thank you" means "danke" :)

@Iambob Don't be discouraged. With a good teacher and/or study methods, I'm sure that after a while you'll get a different perspective on the things that seemed hard or impossible to learn at first. It was the same for me with Chinese, which also has the reputation of being difficult to learn.

Does "den", "dem", and "des" also mean "The" (like along with Der, die, and das) and if they do, how do you know when to use them, and if you don't what do they mean?

See a translation