It's very sad and recently I cry regularly. Don't be afraid of crying, it's good for the soul.
Before my mom passed she said she just wants me to live my life. Do things that make me happy because before you know it life is over. She said: of course you will be sad in the beginning but don't let it control/ruin your life (like it did with my brother, alcoholism), live your life! Do all the things you want to do and don't wait to do it "someday". That memory really helped me a lot with the grieving process and made me realize that life is for the living, let the dead be dead.
I also educated my mom a bit because we never said "I love you" so one day I told her, let's say it! And get over this awkwardness. Since that time (she was already sick) we said it occasionally and I'm very glad we did that. I told her as kids we need to hear these things :)) . That taught me that as kids it's oké to tell your parents your needs. Parents aren't perfect and the're trying their best.
So how do I cope? In my experience the people that are dying are usually afraid that their death will mess up their loved one's lifes permanently and that they are "responsible" for it. So just live life man. That's the greatest thing you can do to honor the ones that have passed. Sometimes you feel like a zombie, sometimes you feel like nothing changed. It's all part of the experience we call life. We are just getting to know more about life and all the sadness and happiness it has to offer.