Hi, I started volunteering when I was sixteen.
I phoned up Oxfam in my area and they let me start almost immediately; I volunteered at Beavers/cubs/scouts thing for a while through an old friend's mum; and the local library runs a volunteer scheme where you can do things like teacher older people how to use computers etc...
There's always summer things, like NCS above and the summer reading challenge... and I know lot's of people at my school, even in younger years, who volunteer weekly at primary schools/nurseries.
But yeah, a good idea is to just walk into the places and ask