My mother-figure died 9:10am, June 20th, 2015 after I spent four days with her in hospice and a protracted hospital stay.
My advice would be to distance yourself from the other people grieving if you're not already really close to them, and to spend your time and attention with the person in hospice. They're probably in shock themselves anyway and it's hard to forgive yourself over missed moments with your loved one.
Read to them, brush their hair, listen to one last story if they can still talk, listen to their final wishes even if it makes you feel like your heart's dropped away. Just, help them feel comfortable, be the one that's /there/. Most of my family members were very self-absorbed during the ordeal; I was the only one that didn't leave her side. Be indulgent, let them have what they want ---- a cigarette, a treat, a chapter of their favourite book, a perfume, a treasured family tale. Help them maintain their routine if feasible, they're probably flustered with all the attention while they're conscious and embarrassed for losing control of any bodily functions if they have. It's frustrating being trapped in a bed like that.
Try to let go of any lingering fears, resentments, emotional pains, or regrets if you can, even if you have to whisper a one-sided conversation while they're asleep. Trust me, you'll feel better for it later.
Feel your emotions. There will be a lot, and it will be very difficult, but try not to be ashamed.
From what I understand, people on hospice tend to want to die alone. Try not to feel guilty if they wait for you to leave.
And absolutely, do not, EVER leave the person on hospice or their medications alone in the room with someone drunk or unhinged. My uncle murdered my mother-figure with morphine almost the hour she got home. So, yeah. Be careful. (I hate that I have to say this, but if it helps you. . . )
Understand that the people around you will be grieving differently. Shock can look a lot like someone isn't griefstricken, too. I didn't cry myself because I was so far into denial.
After they're gone, make sure you start talking to the other people that loved them. Talk about their life, and what they loved, and things they accomplished. Celebrate it as much as you can, even if you're laughing and crying at the same time.
And this is essential, make sure you keep seeking out people that have good vibes, even if you can't talk, even if you're both just sitting in comfortable silence. It's all about that human connection that helps keep us from feeling lost.
Besides that, or if you don't have that, blankets warm from the dryer help, as does a hot mug of coffee or chocolate or tea, even if you don't drink it, and I hope music helps you too. I also enjoy gardens and libraries and rooftops, just try to go somewhere where you feel at peace when you need that. I also like stargazing and reading.
Listen to you if you feel like you can trust you, you probably know what will fill your emotional needs.
Just, don't completely block everyone else out. Even if you can't talk about it, listen to something unrelated just for the company.
When I'm feeling too existential I try to make it positive, that the universe is big and I'm small, but that's not necessarily a bad thing, or that the universe is uncaring, so that means my mistakes don't matter as much as I fear they do.
Allocate someone not panicking, in shock, or in a dissociative fugue to deal with their last wishes if you can. Make sure you talk as a family about what they wanted if their isn't a will, and make sure you spend enough time discussing it despite how upset everyone is that there isn't any mistakes made.
Also, check the reputation of the funeral parlour, and cemetery or crematorium, some of them are SO crooked it isn't even funny.
I hope this helps. It took a long time to type up and it comes from a place of love. I wish you the best in this difficult time, I know it'll be hard. Um, feel free to ask me to listen anytime or to tell me off for not being positive enough, idk, this is what I needed to hear back then, so I really, really hope it helps you.