I think for me having a lot of pets when I was a kid and having them die in all sorts of ways as pets do, taught me about death. We always took time too to give them a proper burial, and it always would involve a short grieving period. (Actually, I would bury dead animals all the time, and we'd visit a lot of old graveyards on holidays, so death was never some far away thing.)
So when actual people started to die during my teens and early twenties, I was prepared in a way, even when it came unexpected. My grandparents passed away, my godmother, who I really looked up to a lot, hung herself, my own mother had a bit of a rock'n'roll death... None of it left me cold, far from that, but it also never turned me into a mess of grief and sorrow. (I already was a mess.) Actually, there was some suicidal threatening going on in the family too when I was a wee lad, so that probably made me keep some distance too.
Maybe it's partly a way to deal with any abandonments issues I might have, but I tend to be aware that anyone who's in my life today, could be gone tomorrow (I am dialing back on that thought though.) Death is part of life, and realizing that makes me appreciate it more. Life that is. A few years ago I was feeling quite sickly and it made me think a lot about what would happen if I died at that moment and then someone would find me. It became a huge motivation in a way. I didn't want to die with my dick in my hand, I wanted to die with my guitar in hand, typing away or making something. Or at least with my dick in someone else's hands, although that wouldn't be very nice to that person, so let's scrap that one.
I guess, to keep it short, I do my grieving beforehand; I'm just that melancholic. Maybe it'll be different when a close friend passes away, I don't know. I just hope it won't happen anytime soon.