Kids become aware of death earlier than you might think. After all, they see dead bugs and animals on the side of the road, and may see animals or people die on TV or in kid-friendly movies. They may even act it out in during playtime. It's a good idea to use examples in nature, like a dead bird, to start a conversation, or discuss a news report about a famous person's death. These talks can help kids get used to the idea that death happens and let them ask questions before it hits close to home.
When a loved one dies, what you say depends largely on the age and maturity of your kid. Death is a complicated, abstract concept that's difficult for very young children to grasp. Avoid saying things like "Grandma took a trip" or "Uncle John went to sleep." Pretty soon your child will notice that her loved one is gone, and she may become terrified whenever you go away for the weekend or fall asleep at night. So tell your child the truth (sparing any upsetting details) and keep your explanation brief. Say that Grandma died and that we won't be able to see or talk to her anymore, since when people die they don't breathe, walk around, or play. Just be prepared to repeat yourself when your preschooler asks "Can we go to Grandpa's house?" three weeks later; young children often think death is temporary and reversible. If the person died after an illness, explain that only very serious illnesses lead to death and that most of the time when people get sick, they get well again.
School-age children can better understand death and experience the grief that accompanies it, although dealing with it for the first time is never easy. If an elderly person died, explain that Grandma lived for a long time but that Mommy and Daddy are still young and so is she. Talking about a young person who died unexpectedly is harder, but it's fine to explain that although her loved one may have been in a terrible accident, for example, these types of deaths don't happen very often.
Regardless of your child's age, once you have told her the news, ask how she feels or if she has any questions. Listen to her reaction and let her know it's okay to cry. Don't feel as though you have to put on a brave face for your child if you've experienced a great personal loss. When grown-ups are open with their sadness and tears, it gives kids permission to follow suit.