http://www.bbc.co.uk/sport/olympics/2012/live-video/p00w2wzb (segment #3)
If you don't have access to it, the salient points of the match are:
48:25, the "sudden death" round is started due to non-combativity or timeouts on the previous rounds. Shin is given "priority" based on the toss of a coin, which means at the end of a minute if no single hits have been scored, she'll win. Shin has been playing much more defensively or tactically all match, so this maintains the tempo up to this point.
49:02, a double-touch happens with 24s left on the clock. Double-touches (ones that occur within 1/25th of a second of each other) are not scoring, so play resumes.
49:27, another double-touch with 15s on the clock. Shin plays very defensively and scores the majority of her points by evasion and counter-attack, but uses up a lot of the piste (the area the fencers are permitted in), so the referees check that she didn't overstep it.
50:09, another double-touch with 9s left on the clock.
50:24, another double-touch with 5s left on the clock. Heidemann isn't scoring a single-touch with her attack, but she's driving Shin toward the back line where she'll lose if she oversteps.
50:48, another double-touch, 4s left on the clock.
51:03, another double-touch happens with 1s on the clock.
51:18, Heidemann immediately attacks the moment the beep occurs for another double-touch with 1s left on the clock. The commentators are bemused that this takes less than a second but to my eye it's pretty reasonable.
51:20, Heidemann and Shin go en guard, with Heidemann repeatedly being warned by the referee not to take a position too close to Shin (the call of "distance" from the ref).
51:39, another double-touch, again with 1s left on the clock. The commentators are wondering about a technical malfunction at this point, but as Heinemann takes her position the clock actually clicks down to 0s. The referee notifies Shin and Heidemann that the clock will be set to a full one second. The Korean coach comes out to argue but is overruled.
52:56, Heidemann scores the single-touch she needs to advance.
Resetting the clock to 1s is actually unusual, if I remember right, and probably shouldn't have happened - I suspect that this was the mistake by the timekeeper (which shouldn't be held against them, Olympic timekeeping is not a "best-effort" thing). It's hard to say who "should have won" the match - Heidemann certainly played a more aggressive and interesting game but Shin's conversion so many of these into double-touches or even points for her are exemplary. As another poster points out, I suppose the real answer is to voice recognition software start the clock on "allez".
Lastly, I just wanted to salute Shin's courage and dignity in coming on to play the bronze match, even though she must have known she had no chance to win the medal. Even having rewatched the match in slow-motion half a dozen times, I have a hard time feeling convinced that the right decision was made - from her perspective she must have felt absolutely robbed.