Here's an example of a sympathy note:
Dear Mary
We were so sorry to hear about your illness. It must have been a terrible shock for both you and your family.
If there is anything we can do to help just let us know.
This note is just to let you know that you are in our thoughts.
With love
If you are writing about a third party you do not know personally you could write (or say):
Dear Mary
I was so sorry to hear about your father's illness. I know you and he are very close.
I just wanted to let you know that you are in our thoughts.
If there is anything I can do to help, just let me know.
With best wishes
If it's a letter of condolence when someone you know has died you might write something like this:
Dear Mary
We were very sad to hear about your father. Please know that you and your family are in our thoughts at this time.
Frank was a real gentleman and a pleasure to be around. We always looked forward to meeting him. We will miss him.
With our love and sympathy