how much; how many; to what extent
Used to ask about quantity, degree, or extent. Can also be used in exclamatory or rhetorical expressions.
どれだけ待てばいいですか。
How long do I have to wait?
どれだけ練習しても上手になれない。
No matter how much I practice, I can't get better.
どれだけの人が来るか分からない。
I don't know how many people will come.
どれほど is more formal and literary than どれだけ, and tends to appear in written or formal speech rather than casual conversation.
どれだけ and どんなに can both mean 'to what extent', but どれだけ often has a quantitative nuance (how much/how many) while どんなに emphasizes emotional degree.
Compound of どれ (interrogative pronoun) + だけ (extent/amount). The kanji spelling 何れ丈 is ateji and rarely used.