Listen, people who are grieving need to share their thoughts and feelings with others.  Don't be afraid to bring up the subject of the death.  If they are not up to talking about it at that time, let them know that you are available if and when they need to talk. 

Offer practical help, like assistance with household chores or errands.

Do not offer false comfort, comments such as, “he’s in a better place now” or "at least you still have your other child", often do not help and can make the grieving person feel even worse.  There is no new baby that can replace one that died, and new puppy that can replace an old friend.  Every spirit is unique and to lose one that you loved can be intensely painful.

Do not pretend to understand exactly how they feel, or try to make it better, you can't.  Grieving is a normal process, the best you can do is to be there for them and listen to them without offering solutions or advice. 

Let them talk it through if, and when they need to.  Being attentive to a persons feelings and needs while they are dealing with loss is the greatest gift you can give.

If your grieving friend begins to cry while talking to you, rather than hugging their tears away, it is sometimes better to lay a caring hand on their shoulder to show your concern and allow their tears and thoughts to continue to flow. Tell them its okay to cry and give them the opportunity and physical space to get it out of their system without smothering them.  Crying is a healthy way to release emotional stress.

Be patient, only after they have had the chance to give vent to some of their anger or sadness, it can be a good thing to lift the mood by distracting them with a different subject or even with some humour to break their tension.  After you have given them ample opportunity to talk and process their grief, it is good to leave them on a lighter note.  You can even change the subject and have a good laugh about some arbitrary thing that happened, rather than leave them on a low note.  If they have had a good opportunity to vent their sorrow and you successfully lift the mood before you end the conversation, they will more than likely stay feeling good for some time before their grief catches up with them again.  The gaps between grieving will become longer as they recover.

Invite them for a sunny walk in a park nearby.  A brisk walk outdoors can be stimulating, energizing and refreshing.