I pretend like they aren't embarrassing situations (usually things people find embarrassing really aren't), force myself not to get embarrassed, and then I move on with my life.
Depending on the circumstance I'll make a big joke out of it and laugh a lot, but that doesn't always work.
For example, if you trip and fall in the middle of a crowd and start laughing about it maniacally, it kind of looks like you're off your rocker. Better to just pretend it didn't happen. If you fart loudly in front of your friends, the best thing to do is run with it. You may end up having a farting contest if you're charming enough (just try not to crap your pants).
Externally: Maintain a calm, neutral face expression, never formally acknowledging the situation. Continuing onward with whatever I was doing without distracting.
Internally: I want nothing more than to burst into tears and return to the safety of solitude, all while indulging in the solace brought forth by fattening foods and The Cure.
This scenario plays itself out at least 7 times a day.