How does "de" help describe a noun?
Three years in high school French and I'm still struggling on understanding how de is used to help a word describe a noun. This is something I noticed a lot, but I couldn't find an explanation to this.
Ex.: du jus d'orange, une drôle d'idée
Update: Fixed article. Thanks for mentioning that.
"De" can help describe nouns by showing possession or specifying the types of things we are talking about. Although it doesn't generally give you a perfect English translation, the best thing about de is that you can translate them to English and still have understandable nouns.
Take your first sentence as an example:
Du jus d'orange ("un" is not the correct article unless you're specifically talking about one juice box) directly translates to "Some juice of orange." Here, you can see that adding "d'orange" shows exactly what type of juice this is contrary to saying "du jus."
The best way I have found to describe when to use "de" to attach adjectives to words is whenever you use a noun as an adjective in English. The reason you would use "de" in the first place is because these formations are not allowed in French, so you'll find that "de" actually has many many uses in these scenarios.
Think about the word(s) "teacher helper." There is no adjective meaning "of or relating to teachers" in French, therefore we must translate this as "assistant de prof(s)" or, directly translated to English, "Helper of teachers."
The same can be done with any word construction like this (though there are some exceptions). For example, you might immediately say "Oh, elementary school teacher, that must be 'Prof d'écoles,'" but there is already a word for that, instituteur/institutrice.
If, by any chance, you have ever studied Japanese, this can be related to the use of the particle "no": の and no-adjectives.
I hope this helps :) If you have any more questions, don't hesitate to ask!