One of my old seniors said that there were several approaches. I think this may be written somewhere in a book but I don't know. The 2 i remember the most are:
1) The crucifixion - basically you get up there and address your attendings "Hello, if you like, i can cross my legs so you save a nail" Take the blame for everything, say you f*'d up big time even if you didn't. This was my preferred approach. Basically if you say that "I suck, i'm a bad surgeon and i can't tie my shoelace much less a tight knot on the aorta" then you give them no where to go. If you beat yourself down so much yourself, the attendings can't really come back with "You f'd up! you suck!" cuz you can just say "yes sir. i already said that in my presentation. Thank you sir. I present my ***** to you now"
it worked for me
2) The Academy Award - i would caution to not try this unless you r a chick (no offense to you feminine men out). Basically you think back to the most horrible event of your childhood (puppy dying, crapping your pants in public, missed opportunity with the hot chick in school) ... anything that will bring the tears out. Then channel your inner actor and poor out the tears as you describe in emotional detail how hard you fought to keep the patient alive who died in your arms as you pounded on his chest screaming "why god?! why!?! TAKE ME INSTEAD!" (this is exaggerated of course, but you get the idea) Basically the end result is that everyone in the room feels so awkward that they won't touch you. The classic thing to do is to walk away from the podium when excused, wipe the tears away, sit down, and wink at the junior sitting next to you with a smirk...classic.
3) Crash Cart or The Code Blue - In this technique, you act so anxious up there, it looks like you're having an MI or if you're a "twitcher", a stroke. Whip out a pill bottle and pop some pills nervously as you walk up for full effect (where's my atenolol?). If you can break out in a profuse sweat at will, then that helps too (go ahead and drench your scrub top, you don't wash them anyway). Again, people in the room will feel so awkward and bad for you that they won't do much to you (for fear of causing your demise). You can't use this one too often. Pick the REALLY bad M&M once every 5 months. Use this technique too often, your PD might think you have a medical condition precluding you from being a good doctor/surgeon or think you're too much of a pu$$y to be a surgeon.
There are others, but these are the ones i saw/used most often
Other general rules
1) Don't blame others. Even if you didn't do it, say you did. Dont' blame another service. "medicine did it..." <pointing finger>
2) learn the lingo. everyone in the room knows when it was an attending call caused the m&m to occur. You can't say "I wanted to save it but Dr. UpMyAss said to cut the ureter". My preferred method is to say "it was discussed..."
3) know your info. If you don't know, don't make it up. If you do make it up, make sure you're consistent and don't contradict yourself!
if you do it right, m&m's can be fun! (for the people in the audience)