We report on an improved measurement of the 2 nu beta beta half-life of Xe-136 performed by EXO-200. The use of a large and homogeneous time-projection chamber allows for the precise estimate of the fiducial mass used for the measurement, resulting in a small systematic uncertainty. We also discuss in detail the data-analysis methods used for double-beta decay searches with EXO-200, while emphasizing those directly related to the present measurement. The Xe-136 2 nu beta beta half-life is found to be T-1/2(2 nu beta beta) = 2.165 +/- 0.016(stat) +/- 0.059(sys) x 10(21) yr. This is the most precisely measured half-life of any 2 nu beta beta decay to date.