Ok, so I found both of my preceptors/mentors in fortuitous ways, and that's probably how it will happen for you, too. My first preceptor happens to be my personal ob/gyn--and she offered to let me shadow her while she was performing my Pap! (True story--I even used that as the opening for my admissions essay.) My second preceptor was my friend's doctor, and she introduced me to him.
In my experience, there is no point in sending out resumes or trying to call offices of doctors you've never met. I tried both of these, and I got ONE shadowing experience out of it. And it was a bad one (see arrogant neurosurgeon in my previous post).
So, the rule of thumb is: ask doctors you already know. Don't worry about it being awkward--if I can shadow my ob/gyn and then go back for my annual, you can shadow your old pediatrician!
If it doesn't work out with any doctors you know, or you've managed to go through life until now without encountering a doctor (??) move onto the next steps.
Shadowing a doctor you don't know
It's time to get over being shy. When you meet doctors, from this point forward, stick out your hand, introduce yourself (full name), and say you are planning to apply to medical school. You'll usually be able to read the doctor pretty easily at this point, in terms of wether they are the teaching type or not. They'll either get very squirmy and awkward or they'll start asking you ALL about your plans.
If they are the latter type, come right out and say, "I'd really love to shadow you. Do you allow students to shadow?" If they say no, it's usually because of a facility rule or because they already have too many students. If that's the case, ask if they have any colleagues who enjoy teaching.
So, I know this can be awkward and it feels like begging for scraps, but you just need to start asking for help from every doctor you meet. Seriously. Every one. The thing with shadowing, and with medicine as a career, is that it's all about connections. I hated this and resisted it for a long time, but it's just a fact. The more people you know, the more resources you have. This will help you learn, get into school, get a job, and, most importantly, take better care of your patients!
And ask ME for help! Please let me know what other questions you have. I write this for you guys! Comment below or email me: email@example.com.