I haven't played vanilla survival for some time, but I think that dungeons have been becoming more and more rare with each update (or maybe it's just my imagination).

If you're having trouble finding them, I'd recommend going to a desert and looking for caved-in dungeons.

Otherwise, you'll just have to keep hoping to come across one of them while mining.

You can edit how rare they are by choosing a custom map style and changing the slider.