Even if it's very unlikely that any one atom will decay at any given time, and it will take Brazillions of years for all to decay, if the sample is large enough and your instruments sensitive enough you can monitor a sample for months and get enough recorded decay events to extrapolate the half-life -- the longer you take measurements, the more precise the extrapolation. Also, the larger your sample, the faster you accumulate data -- these guys used 3,200 kg of liquid xenon. 
They should have observed a pretty large number of decay events -- enough to lower the statistical uncertainty pretty quickly. Oh, and placing the experiment inside a mountain helped shield the detectors from cosmic rays and other background radiation.
(In small amounts, Xe costs ~ $1.20/g, or $1200/kg, for anyone who's thinking of repeating this experiment.)
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