Based on the level of respect or formality, you can say "How long have you been studying Korean?" in Korean in 3 ways:

• Informal: neo-neun hanguk-eo-reul eolmana gongbu hae watseo? (너는 한국어를 얼마나 공부 해 왔니?)
• Formal: dansin-eun hanguk-eo-reul eolmana gongbu hae watseoyo? (당신은 한국어를 얼마나 공부 해 왔어요?), dansin-eun hanguk-eo-reul eolmana gongbu hae watseupnigga? (당신은 한국어를 얼마나 공부 해 왔습니까?)
• Very Formal: dansin-ggeseo-neun hanguk-eo-reul eolmana gongbu hae osieotseupnigga? (당신께서는 한국어를 얼마나 공부해 오셨습니까?)

- how long: eolmana (얼마나)
- you (subjective): ne-ga (네가), ni-ga (니가), neo-neun (너는), dangsin-eun (당신은), dansin-ggeseo-neun (당신께서는)
- to study: gongbu hada (공부하다)
- Korean: hanguk-eo (한국어)

Please refer to How to pronounce Korean Alphabet for the English pronunciation in this answer.