Preverbs can be surprisingly independent. Usually they would be around their verb because they indicate a movement and that makes little sense without a verb, but here, in this phrase, there is no verb it can attach to. It's not an actual sentence.
A bit like in English, actually: "We go away from somewhere." The 'away' is practically a part of the verb, modifying it as its adverb.
This incomplete sentence could be used, for example, in an emergency situation. The building is on fire, or it is about to collapse, etc: Away from the building!!! That is, please move away from the building. Hungarian works quite similarly in this regard. The preverb expresses so much, the verb is omitted.
Another example, although expressed differently in English:
"Fel a kezekkel!" - Hands up!
That is literally: "Up with the hands!"
I don't understand the subtle difference between elative -bol and ablative -tol. In a previous lesson we had "épületből" and now "épülettől" but both cases seem to mean "movement away from" (building, here). Is there an actual logic here, or difference in meaning, or is that just a matter a learning certain combinations of verbs/nounds/cases because that's just the way it is ?
You should think of them as parts of two different trios.
-ből, -ben, -be mean "from out of / in / into". When they indicate location, they're talking about something you can be inside - motion out of it, location inside it, or motion into it.
-től, -nél, -höz mean "away from / at / toward" when they are indicating location.
So el az épülettől might be used if you're hanging around outside the building and someone wants you to "go away from the building."
But ki az épületből would be used by somone telling you to "come out from the building."
There's also a third trio: -ről, -n, -re for "off of / on / onto"
So for location we have 9 endings:
-ből, -ben, -be answer "whence, where, whither?" "from out of / in / into"
-től, -nél, -höz answer "whence, where, whither?" "(away) from / at / toward",
-ről, -n, -re answer "whence, where, whither?" "off of / on / onto"
Looking a little further ahead, there are verbs that use these endings in non-locative senses, and those you do just have to remember. For example, "to be afraid of something", is translated as fél valamitől, and you just have to remember that fél commands the -tól / -től ending.
"To remember something" is emlékszik valamire and, you just have to remember that emlékszik commands -ra / -re.
Hungarian is just very specific with its start and end places of a movement. And since its time is rather flexible it looses sync with English. English is ambigious of the where exactly, Hungarian is ambigious about the when.
"épületből" "épülettől" are clearly different in regard to where you started. In the present English is very much the same. You move out of the building or away from the building. If this action continues though, Hungarian sticks to the starting place and it is still "out of" (although you are not in that process anymore) but in English from the building. In English on the other hand you just specify that you were somewhere near the building, inside or not is not the important information. Later you always move in the "second now", away from the building while Hungarian still differentiates.