Mod Note (Andy): You can read his ongoing AMA here: "BB Operations MD AMA"
We all know that the best person to push your resume for a internship at a BB is the MD. We have a high amount of authority and really can get someone in who might have less than stellar experience or some mediocre state school and/or poor grades.
How you want to convince the MD starts with the introduction of yourself. Make sure your linkedin and resume are solid (ie wear a suit in your profile picture) and check for any discrepancies between what you put on your resume and linkedin profile. Create a template cold-email and send it off to a couple analysts first to test the waters. I highly recommend you befriend someone who is a English major to help with any issues you didn't catch when you made the template. Try to send emails to the MD who has a common interest or affiliation.
Once you have set up a time and day to talk or meet you can start practicing what you would like to ask. Don't ask obscure questions or irrelevant questions that don't relate to their job or interests. You can have a cheat sheet if you are on the phone so you won't go off topic. You can also add simple reminders for any technicals you know that may surprise the MD who may not think you know as much yet.
When the call is over you should email them periodically (ie not every 2 days) to keep them updated and/or interested with how things are going. I don't want someone to network with me and then email/call me 6 or more months later asking for a job.
Read about how to be persuasive and friendly to people of authority and don't act in awe of the MD. We're just like everyone else you will ever meet. Unless the MD is a complete tool I don't think feeding his ego will work. NEVER lie to a MD. Doing this is probably the easiest way for me never to speak to you again. It's one thing to stretch your experience but if you put investment experience on your resume but can't explain p/e ratios you will be finished by the MD.
When recruiting season comes up and you just applied for the BB internship online, try to play dumb and ask the MD if he knows anyone who can push your resume for the spot. If you've already known him for a while it will make things much easier. He will probably push your resume for you if there's a solid connection.
(PS: Cold-calling for local firms will work better. They're more likely to be excited that you're interested in them.)