Just being present, "heart with ears" is often the best way to help someone who is hurting.  We all need to share how we are feeling.  Often without words.  If anything is to be said, if appropriate, "I'm SO sorry for your loss" (that's all).

Ask the person how they are doing.  No one can know how they are feeling, their relationship and feelings are unique to them.  There is no comparison.

Consider asking if they would like any help with a task, appointment, maintenance, etc.  Leaving the offer open if they say 'no' at first.

Firsts can be extra difficult for the griever.  Remembering the special memories, first holiday, anniversaries as well as the date someone died. 

Feel free to invite them to a meal, without any expectations including offering a plate if they aren't up to attending.

I often hear from grievers that (especially around the holidays and special events), that people never mention the missing loved one's name.  Consider some questions - What was a special memory for them?

Letting the griever know - that they can share stories.

That it's okay to cry or not cry.

That it's okay to laugh and chuckle.

Looking at pictures can be healing.

Some people find it helpful to have an 'empty' chair at the table.

Please know that healing in grieving, doesn't mean you forget the person.  Instead it gives you a toolbox to move forward from that.

Giving them the Grief Recovery Handbook and/or https://www.griefrecoverymethod.com at the Grief Recovery Institute has resources and links as well.