Re: Grief -
I generally find that one of the worst things people go through other than the pain of the loss itself is no one else knowing how to act around them and/or being weird about it, even though it happens to literally everyone at some point. It feels so horribly isolating, at least to me.
My tactic, rather than trying to use platitudes, is generally just acknowledging how horrible and shitty this is and that it's probably going to be horrible and shitty for awhile -- but that they're not alone, have people that care about them, and can ask for help, even if that help is just unloading if they want to.
Same goes for scary medical diagnoses, bad financial problems, or serious relationship breakdowns. I don't think I've ever once had someone respond badly to that. Most honestly seem relieved to have someone not expect them to pretend to be okay for the sake of public appearances . I've ended up having a serious bonding moment more than once, even with coworkers.
If you are in a position to offer help, I recommend going over and just taking on some mundane task for them so they have one less thing to try to brain about when they're stressed and/or numb. Even when people have the very best of intentions, it can be hard to muster up the mental energy to figure out what needs doing, let alone parcel stuff out.