The question phrase "how long" is usually expressed using by any of the following: どのくらい and どれくらい. This source says that, according to the 日本文法大辞典, どのくらい was commonly used in the Edo era, but どれくらい became more common in the Meiji era. Google Search shows that both are still commonly used today. くらい is loosely translated as "about" or "approximately".
Dono kurai/dore kurai machimasu ka?
How long will we wait?
Anata wa Nihon ni dorekurai sunde imasu ka?
How long have you been living in Japan?
You can also be more specific by using 何日、何時間、何ヶ月, and so on.
Mainichi, nanjikan, shigoto wo shimasu ka?
How many hours do you work every day?
Nannichi gurai taizai shimasu ka?
About how many days will you stay?
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