It's never too soon to introduce caring about others and the community. Your kids will imitate your actions so let them see you engage. It takes time, but it is quite simple. As you go about your charitable and community building activities, bring the kids along. At a certain age, they can be plopped at the back of a board room with crayons or an iPad. They won't hear or understand much (or anything) that is going on, but they will recall that their parents find it important to be involved in community activities.
As children get older and you decide they're ready to receive an allowance, require that they divide their allowance into two or three pots: to spend, to save... and to donate. You can simply give your child three jelly jars or purchase items designed for this purpose, such as Moon jars. Then, once a year, ask your children what they care about — animals, children who need health care, people who need housing — and help them donate the money.
Make it a family event to volunteer — collecting tickets at the PTA carnival, serving a meal at the homeless teen center, participating in clean-up day at the local park or beach. Volunteering as a family reinforces shared values.
When you think the time is right, provide a small amount — $100 - $500 — to your children and have them work together to determine where it should be donated. (A good way to learn how to make decisions — and compromises.) You can even ask fellow foundation trustees, other family members or good family friends to serve as philanthropic mentors to your kids.
There are some formal youth philanthropy programs where teens serve on grantmaking boards. Youth Philanthropy Connect is a national organization. Community foundations and Social Venture Partners are two places to look locally for these (the links lead to examples in Seattle), or go to Learning to Give for other ideas.