“Have you taken up painting?”

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?

have you (done something)?

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?

take up (a hobby)

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.