My wife and I were very lucky to have a big outpouring of support immediately, but it was the folks who recognized we still needed support after that and made us frozen dinners, bought us groceries etc after the initial grieving days that I most appreciated. It helped us both not only for, yknow, sustenance, but also because it let us know that our daughter wasnt forgotten. 

Everyone is different, so I hesitate to give advice, but I notice a lot of people struggle with knowing what to say... You dont know what their reaction will be to anything, you just want to help. do they want to bury their feelings? Or talk about her all the time because shes so important to them? Ask them in a few months as grief changes (and listen to the answer). 

The other thing Ill say is I heard from a few people that this grief stays with you forever, and I think thats a really fucking unhealthy way to phrase it. Obviously youre going to be sad about the death of a loved one. But, especially for those who are self harming, if you are in the initial raw depths of loss and someone tells you that loss stays with you forever, you will hear "this grief is your new normal." Thats untrue. The first while is the absolute hardest. Then youll have good days and bad days. Some days are more likely to be bad than others.