Is generosity something that is taught or does it just come naturally? I'm no scientist, but the innocence and unspoiled nature of children tells me that they are just as likely to do good as anyone. If we teach them of the many benefits, it certainly can help them along the way. (Sadly children also see so much bad around and can certainly pick up those habits too).
Involve your child in your own giving and tell they why it is you give. If you normally place cash in a church offering plate for example, you might explain the practice to your children and then let them do it too.
There are so many ways to give, but think of some that involve children or that would be fun for children to do and then get your own kids involved with you. You can go on a trash walk and clean up a local park for example or plant a tree. Do a yard sale, and give the proceeds to a local charity. Put together a birthday bag for a child living in a shelter. Volunteer or donate to a local food bank. Read to children at your local library. Be a big brother or a big sister. Share information about your favorite charity.
Start giving early? I think it's a great idea!