"What's on your mind" ("what're you thinking about", etc.) can be a more effective prompt/question, than "how are you feeling?" It's a sneaky little CBT trick, but it often works - it's often easier for people to say what's on their mind - their thoughts - rather than pin down their feelings. Since thoughts and feelings are interconnected (that's the CBT part: one leads to the other, in either direction) - you're encouraging the individual to practice separating them.
(Also: "how are you feeling" can be a dead-end question, when someone is feeling badly.)
For the more explosive sufferers - giving them options: "what would be good right now - distraction, sharing, or quiet?" It lets you offer help without you (inadvertently) requiring that they take it.