You visit your aunt's house. There's an easel set up in the corner of one of the rooms, but you've never heard about your aunt painting before. You ask her:
Oh, have you taken up painting?
Asking "Have you...?" is better than "Did you...?" when you are asking for general news about a person's recent life:
Have you lost weight?
Have you seen "Avatar" yet?
Have you called your mother lately?
This is the most common way to describe starting a new hobby. It can be used with the words "a hobby":
If you feel bored, why don't you take up a hobby?
Or it can be used with the name of the hobby:
My parents have recently taken up gardening.
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