lang
long
Having a large spatial extent in one dimension.
Der Nil ist ein sehr langer Fluss.
The Nile is a very long river.

long
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long
Having a large spatial extent in one dimension.
Der Nil ist ein sehr langer Fluss.
The Nile is a very long river.

To describe movement along a route, 'lang' can stand after the noun. In this case, the noun is in the accusative. This word order is a special feature.
Wir sind die ganze Straße lang gelaufen.
We walked all along the street.
Whether 'lang' describes a spatial distance or a duration of time can be recognized from the noun. Words like 'Weg' (path/way), 'Schlange' (line/queue), or 'Hals' (neck) point to a spatial meaning. Words like 'Zeit' (time), 'Tag' (day), or 'Woche' (week) point to a time-related meaning.
Die Warteschlange vor dem Kino war sehr lang.
The line in front of the movie theater was very long.
In connection with time, 'lang' is often combined with verbs like 'warten' (to wait), 'dauern' (to last/take), or 'suchen' (to search). A common expression is also 'ein Leben lang' (for a lifetime), to express that something applies forever.
Wie lange dauert der Flug von Berlin nach New York?
How long does the flight from Berlin to New York take?
The idiom 'lang und breit' means 'very extensively' or 'in all details'. It is often used with verbs like 'erzählen' (to tell), 'erklären' (to explain), or 'diskutieren' (to discuss).
Sie hat mir lang und breit von ihrem Urlaub erzählt.
She told me about her vacation at great length.
The expression 'sich lang machen' is a colloquial and reflexive phrase. Depending on the context, it can mean 'hinfallen' (to fall down) or 'sich zum Ausruhen hinlegen' (to lie down to rest).
Pass auf, dass du auf dem Eis nicht hinfällst und dich lang machst!
Be careful not to fall and go sprawling on the ice!
for
'für' and 'lang' can both express a duration. 'für' comes before the time expression and often states how long something is planned for, valid for, or lasts: 'für eine Woche' (for one week). 'lang' usually comes after the time expression and emphasizes the length of the duration: 'eine Woche lang' (for one week / one week long). The words are therefore easy to confuse, especially with expressions like 'zwei Tage' (two days). Often both are possible, but the sentence structure is different. You say 'für zwei Tage' or 'zwei Tage lang', not 'für zwei Tage lang' in simple standard sentences.

Wegen des starken Regens warten wir fast eine Stunde lang auf den Bus.
Because of the heavy rain, we wait for the bus for almost an hour.
Am Morgen lernt ihr für eine Stunde neue Wörter.
In the morning, you learn new words for one hour.