One such sentiment that so many so often use is "let me know how I can help," or variations of the same. While I fully believe that those who say this do so sincerely, it often takes too much effort on the part of the griever to take others up on this offer. When you are in the midst of a crisis of any kind you are bombarded by things that need done, emotions, and-- often-- well-wishers. In any situation this is overwhelming, but when grieving it can be especially so. I suggest just go and do, instead of offer. I have had many experiences with such generosity. For example, after I broke my arm I wasn't about to ask for help, but my mom, aunt, and a great friend all brought me dinners during the first week so I didn't have to cook. They didn't ask or vaguely offer to do it, they said they were going to do it, and on which days, and then did it. It was such a blessing and relief to have that help while I was trying to figure out how to do everything with one hand. If you want to help choose something you want to do, when you want to do it, and then check with the person(s) that it will work for them.
It is also good to know that the people that are grieving are uncomfortable too. From the outside looking in it is hard to know what to say or do, but it is the same on the inside. It's hard to know how to respond to people, it's hard to know what to do in the situation, and it's hard to think ahead to answer many of people's questions, or how life is going to go on after the funeral (or other event) is over. Sometimes the grievers meet new people and it gets uncomfortable again as these new people learn about the grief. Other times situations arise that cause the grief monster to rear its ugly head and this can cause discomfort too.
Sometimes the best way to deal with all this discomfort is to just start talking. Those of us who are grieving are not all that different from those who aren't plagued with this monster. We want friends and companionship, it's just a little harder for us when people who don't know what to say avoid saying anything (or avoid us all together). Some people don't realize they are avoiding someone who is grieving, and sometimes we don't realize that we are being avoided. It is uncomfortable and difficult all around. Just realize that a person dealing with grief is often more introverted and less likely to start a conversation and take the initiative-- they will probably thank you for it.
Another part of all this grief and child loss business that often makes people uncomfortable is how/if to talk about the lost child. I realized, a year and a half ago, that I need to talk about Ethne. I need people to know that she
More than anything patience is the key. Some days a grieving person will seem normal and happy and others we may not be able to get out of bed. Be accepting and realize that, we really are fairly "normal" and have many of the same wants and needs as everyone else. Be our friend, and realize that, just like you, things may be difficult or uncomfortable for the griever too.