It is always wise to offer a grieving person your condolences via a phone call and a written card. You should call that person as soon as you hear about the death in her family and then you should follow up with a sympathy card. If you'd like you may buy and send a preprinted sympathy card but never just sign it as is. You must always add a handwritten note to this card, even if it's just to say “I'm so very sorry for your loss.”
Beyond sympathy cards, there are many ways that you can offer someone your condolences. You can offer to help her with any funeral arrangements she has to make or little odd jobs that will make her life easier before, during, and after the funeral. This might be going grocery shopping for her, helping her to clean her home for the open house she's planning to have after the burial, or just making yourself available for a cup of coffee from time to time.
Sending flowers is another great way to offer condolences. You can send a traditional funeral wreath to the funeral home or you can send some kind of greenery to the person's home. Like with a sympathy card, you want to do more than just sign your name to the card that comes with the flowers. Again, all you need to do is add a personalized line, such as “We just wanted you to know that we're thinking of you.”
Do not send flowers if the mourners have asked people not to send them. You need to respect their wishes. Consider sending a donation to a charity if that is what the family has requested in lieu of flowers.
Many people offer condolences by making a donation to a good cause in the name of the deceased, especially if the family asked for donations in lieu of flowers. If they didn't and you'd like to make this gesture, you can send money to that person's house of worship or favorite charity.
In the Catholic religion, it's traditional to buy and send a Mass card to the deceased person's family. The church where you got the Mass card will say a Mass in that person's name in the near future, and devout Catholics often feel great comfort in attending the Mass said in their loved one's name. (The Mass card will provide the exact date.)