"A high tree is standing at the lake."
Translation:Ein hoher Baum steht am See.
Hmm, in the case of seas, lakes and rivers it's virtually always 'an'. At the moment, I can't think of a counter example: 'Am Gardasee, Frankfurt am Main, Frankfurt an der Oder, Wir machen Urlaub am Mittelmeer. Das Haus steht am Fluss. Wir grillen am Meer'. In the case of neighbouring cities we virtually always (again, I'm not aware of any counter example) use 'bei': "Bernau bei Berlin". Let me think a bit... EDIT: Couldn't find any counter examples. So, 'use "an" if water is involved' might be a good rule of thumb. For cities you can safely default to 'bei' and for buildings usually both are possible. For people use 'bei'. BTW: do you know of http://tatoeba.org/eng ? You usually can find a fair amount of sample sentences there.
When I read this sentence I instantly imagine a tree near a lake. The next task is to say that in English or in German :-) I don't see much difference between English "at" and "by" in this case (in fact, I'd prefer "near") and I have not yet figured out all the subtleties of "an" and "bei" in German.
I tend to think at life depending from water, hanging at rivers and seas and oceans...
If you consider water as a source of life, maybe it's easier to think it as "an"... Everything that is next to water, is hanging at it, like "ein Bild hängt an der Wand".
I must be crazy, I have weird ways to remember things. :D