For some reason, my pre-med advisor was very reluctant to give me any help in this field...so here's what I did:
I made up letterhead for myself on Microsoft Publisher with all of my contact information. I wrote a brief letter stating my career interests, academic background, and why I would be so incredibly grateful If I could shadow with ____. I included a resume as well. I found names of all of the doctors in my area via the phone book. I sent these letters and resumes to all I was interested in shadowing. After about 10 days to two weeks, I made follow up calls. Sure enough, a few of the practices I sent letters to had circulated the materials around the doctors in the practice and a few doctors offered times that I could come in and shadow. Conversely, a few of the places I called gave me the whole we'll call you back later run-around and nothing happened. But, I did get the opportunity to shadow two very good doctors by doing this, so I'd recommend this approach.
Kidding aside, you'd be surprised what activities doctor's like to get involved in. I've met a couple through this social interaction. This is often a better approach than stalking them around the hospital. Get to know them outside of the hospital. I did and it's been a fabulous experience. If you can, try to become friends with them. Plus, I sent a letter to another doc about shadowing. He was an osteopath just for the record. He called me a week later. He told me that not only would I get to shadow him, but his colleagues...one of which is a thoracic surgeon, who by the way, performed a lung transplant that's only been done 15 times in the world! I was like WOAH!!! 
