Whenever there is a death in the family, it is a time of intense grief. It is in most people's nature to want to reach out to their bereaved friends in their time of sorrow and need. However, knowing exactly what to say can be problematic, as it is a natural tendency to rack your brain for the perfect way to express your sympathy. Your words need to be chosen carefully, but there are ways to easily and adequately convey your sentiments with a few simple words.
Convey your sympathy right off the bat. A simple "I'm sorry for your loss" or "you're in my prayers" says a lot. There is more to be said, but expressing your sorrow for their loss first is important.
Offer to help. Sometimes, this means just being there to keep them company. Other times, it can mean that they need you to take care of a few errands with the funeral. Either way, your assistance will be much appreciated.
Tell a short story about a pleasant, shared event with the deceased. Given the limited space of sympathy cards, the anecdote obviously needs to be brief. But a simple "I'll always remember how he took me to Disneyland" type of statement will mean a lot to the grieving family member, knowing that their lost loved one meant a lot to you.
Keep it simple. A little bit goes a long way, and it's important to speak from the heart without excessive rambling. Plus, the fact that you sent a card to begin with lets them know that you care and are there for them.