I used to ask families how much they wanted to know...and then provide that information in a caring, compassionate way. It allowed them to have some control over an uncontrollable situation.
Look up mindful listening...there's quite a bit on that topic. Practice the techniques because it can be hard to simply listen...we often want to jump in and say something(anything) when the family/patient just need us to hold the space for them.
Kudos to you to looking to improve your practice...I'm sure you're doing fine and will continue to provide compassionate care!