I was wondering how to ask my family how they handle money when growing up. How can I ask on a sensitive topic?

Put it to them as a question. i.e I am planning on saving for the future and I was wondering how you managed it (for example)

I am glad this question came up because as I am getting older and tackling adult responsibilities I realized I have been trying to get this answer myself. In the middle of talking to my parents about my future goal including school, work, buying a car, and eventually moving out, I finally asked. I started with asking how much money they had when they knew it was time to move out. Then we went into details regarding how to manage your money, learning from both what helped them and what they learned from. There is no correct answer but rather lessons to take with you.