We study a surveillance wireless sensor network (SWSN) comprised of small and low-cost sensors deployed in a region in order to detect objects crossing the field of interest. In the present paper, we study two problems concerning the design and performance of an SWSN: optimal sensor placement and algorithms for object detection in the presence of false alarms. For both problems, we propose explicit decision rules and efficient algorithmic solutions. Further, we provide several numerical examples and present a simulation model that combines our placement and detection methods