This is a very informative article on offering condolences. Quite often people do not know what to say, what to write, what to do. I like the suggestion of sharing memories. If you know the person who died well enough; I am sure you can think of a good memory to share.
‘Remove yourself from the conversation’ is also a very good suggestion. When someone is grieving they do not want to hear about you and your loss, they want to talk about their family, friend, pet who died; again catch yourself and share a memory instead.
Another article- Why Not to Say ‘How Can I Help?’ to the Grief-Ridden
Don’t ask the bereaved what you can do — just do something by Jill Smolowe.
Also a very good article with great advice and suggestions, do vs. asking. Quite often the bereaved cannot answer that question. Bring food, pick up the kids, take the dog out, go grocery shopping, clean, do the laundry……. DO vs. Asking what to do.