I'm not sure how other portrait artists work, but for me it's a case of getting to know my subject a bit better. If I've met my subjects then it's a bit easier to interpret them in my painting. Sometimes I'm able to convey a little something that was not in the photo. Then there are the times I'm required to paint purely from the photo, I can do that too, but then it just becomes a reproduction of the photo. Maybe it sounds silly, but that's the way it works for me.
If the painting is of someone I've not met, I will ask for other photographs of them to see them from different angles etc. I will try to find out more about the person's personality and so on. All these things help me to create a portrait of the person, and not just a reproduction of the photo.