How to Comfort Someone After a Loss

First of all, you need to realize that you may not be able to comfort them the way they want to be comforted. Accept that now. Otherwise, just be around. Less observations and more just being there. Keep observations about the dead guy to a minimum (if at all), they aren't wanted, especially if the person was a turd (everyone's magically perfect when they die).

Keep them company. Reach out, let them know you're here for them, offer a distraction. If you know them in real life, bring them food, preferably stuff that will last a while. Help them keep their place tidy and sort through the stuff their loved one owned, if your friend is okay with that. When someone's grieving, it often leaves them with very little energy to do things like cook and clean. If you knew the loved one, talk about your memories with them and any positive things they said/felt about your friend. If you have any pictures, ask if your friend wants them.