The ALPHA experiment has succeeded in trapping antihydrogen, a major milestone on the road to spectroscopic comparisons of antihydrogen with hydrogen. An annihilation vertex detector, which determines the time and position of antiproton annihilations, has been central to this achievement. This detector, an array of double-sided silicon microstrip detector modules arranged in three concentric cylindrical tiers, is sensitive to the passage of charged particles resulting from antiproton annihilation. This article describes the method used to reconstruct the annihilation location and to distinguish the annihilation signal from the cosmic ray background. Recent experimental results using this detector are outlined.