I hated these at first.
There are a million of them and they seem so hard to distinguish: davon, dafür, darüber, damit, danach, dazu, dabei, dadurch, and on and on and on oh lord. I confused them constantly, I didn’t even really understand what they were for, I didn’t know when to use which one. I treated them as individual, unrelated words whose definitions simply had to be memorized one at a time. I did not see the pattern.
Now look, this is actually really easy (and embarrassingly obvious once you see it): it’s just a shorter, easier-to-say, substitute for what you were previously talking about. Context is vital for these to work, they absolutely do not function on their own – this makes it easier for us, not harder, since we can use context to help us and don’t have to just memorize a definition.
We do it in English
More frequently in old-timey English, but a few have still survived to the modern day.
And there are plenty more. Most of these aren’t used anymore, and the majority of those that are, aren’t used very often. Start analyzing them by seeing first the overall meaning and then looking at the individual words that make them up (hereby = here + by) and their definitions, then see how it actually makes sense. For example: thereby means “because of that”. “By” can mean “because”, e.g. “By eating too much, I got fat”. “There” refers to the preceding that you’re now speaking about (didn’t I say context was vital with these?), so “thereby” means “by there [something happened]”, e.g. “I ate too much, thereby getting fat”. “Therein” just means “in that thing I was just talking about”. “There” + “in” – do we really need to analyze this one? “Therein lies the problem” – that means the thing we were just talking about has (contains…in it) the problem. In there the problem is. “Why are you fat?” “I ate too much. Therein lies the problem.”
Back to German
“Da” means “that” – what follows is a preposition such as “for”, “to”, “about”, “from”, “with”, etc. This forms a compound word that means simply “preposition + that”, e.g. “for that”, “from that”, “to that”, etc. The correct preposition to use, and therefore the correct “da-word” to use, is determined by what you were talking about and what you’re now doing to it (are you doing something with, to, for, by, after, or from it?).
“von” means “from/of”, right? Ok, well if you want to say “of/from that”, then you use “davon”. A common way of saying that you haven’t heard of something in German is “Davon habe ich nicht gehört”, literally “Of that have I not heard”.
“über” means “about” or “over” (depends on context), right? Ok, well “darüber” just means “about that” or, less commonly, “over that”. The way you say that somebody was talking about “that” in German is, “Er hat darüber gesprochen”, meaning “He talked about that”. Talked about what? Well that depends on what the preceding conversation was, what the context was, like I said. Ok, so let’s have a look at enough speech that it actually makes sense:
“Der Lehrer sagte mir, das die Prüfung abgesagt war.”
“Ja, er hat darüber im Unterricht gesprochen.”
“The teacher told me that the exam was canceled.”
“Yeah, he talked about that in class.”
I hope that helped some people, let me know what I could do better (or plain screwed up) in the comments.