I have gotten most of my shadowing experience by asking family friends, friends' parents, neighbors etc. However, one of the hospitals where I live has a shadowing program that high schoolers and college kids can do. It's a half day that you apply for a few weeks in advance (they have it about once a month). Check out the websites of places near you.
Also, I'm planning to ask my pediatrician at my next visit and see if she will let me shadow on a day off school.