This paper considers millimeter wave (mmWave) MIMO communication systems that employ analog beamforming. We propose a new two-phase beam acquisition algorithm for the practical multiuser scenario. The algorithm is based on efficiently searching beamforming codebooks at the base station (BS) and the mobile devices (user equipment, UE). In the downlink training phase, the BS broadcasts a training signal and each UE performs a search of its codebook. In the uplink training phase, we develop a multiuser iterative beam search method in which the BS simultaneously finds the beam directions of each UE. We also examine the trade-off between training time and the number of users acquired, with a practical frame structure protocol. Numerical studies demonstrate up to 38% reduction in acquisition time, compared to direct application of single-user approaches. In addition, our approach finds the best beam for each UE with up to 14% more accuracy, which results in higher spectral efficiency in the subsequent data transmission.